Algebra Examples

x^{4} - x^{3} + 2 x^{2} - 4 x - 8 = 0

$x^{4} - x^{3} + 2 x^{2} - 4 x - 8 = 0$

Step 1

Factor the left side of the equation.

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Step 1.1

Regroup terms.

- x^{3} + 2 x^{2} + x^{4} - 4 x - 8 = 0

$- x^{3} + 2 x^{2} + x^{4} - 4 x - 8 = 0$

Step 1.2

Factor

- x^{2}

$- x^{2}$ out of

- x^{3} + 2 x^{2}

$- x^{3} + 2 x^{2}$ .

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Step 1.2.1

Factor

- x^{2}

$- x^{2}$ out of

- x^{3}

$- x^{3}$ .

- x^{2} x + 2 x^{2} + x^{4} - 4 x - 8 = 0

$- x^{2} x + 2 x^{2} + x^{4} - 4 x - 8 = 0$

Step 1.2.2

Factor

- x^{2}

$- x^{2}$ out of

2 x^{2}

$2 x^{2}$ .

- x^{2} x - x^{2} \cdot - 2 + x^{4} - 4 x - 8 = 0

$- x^{2} x - x^{2} \cdot - 2 + x^{4} - 4 x - 8 = 0$

Step 1.2.3

Factor

- x^{2}

$- x^{2}$ out of

- x^{2} (x) - x^{2} (- 2)

$- x^{2} (x) - x^{2} (- 2)$ .

- x^{2} (x - 2) + x^{4} - 4 x - 8 = 0

$- x^{2} (x - 2) + x^{4} - 4 x - 8 = 0$

- x^{2} (x - 2) + x^{4} - 4 x - 8 = 0

$- x^{2} (x - 2) + x^{4} - 4 x - 8 = 0$

Step 1.3

Factor

x^{4} - 4 x - 8

$x^{4} - 4 x - 8$ using the rational roots test.

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Step 1.3.1

If a polynomial function has integer coefficients, then every rational zero will have the form

\frac{p}{q}

$\frac{p}{q}$ where

p

$p$ is a factor of the constant and

q

$q$ is a factor of the leading coefficient.

p = \pm 1, \pm 8, \pm 2, \pm 4

$p = \pm 1, \pm 8, \pm 2, \pm 4$

q = \pm 1

$q = \pm 1$

Step 1.3.2

Find every combination of

\pm \frac{p}{q}

$\pm \frac{p}{q}$ . These are the possible roots of the polynomial function.

\pm 1, \pm 8, \pm 2, \pm 4

$\pm 1, \pm 8, \pm 2, \pm 4$

Step 1.3.3

Substitute

2

$2$ and simplify the expression. In this case, the expression is equal to

0

$0$ so

2

$2$ is a root of the polynomial.

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Step 1.3.3.1

Substitute

2

$2$ into the polynomial.

2^{4} - 4 \cdot 2 - 8

$2^{4} - 4 \cdot 2 - 8$

Step 1.3.3.2

Raise

2

$2$ to the power of

4

$4$ .

16 - 4 \cdot 2 - 8

$16 - 4 \cdot 2 - 8$

Step 1.3.3.3

Multiply

- 4

$- 4$ by

2

$2$ .

16 - 8 - 8

$16 - 8 - 8$

Step 1.3.3.4

Subtract

8

$8$ from

16

$16$ .

8 - 8

$8 - 8$

Step 1.3.3.5

Subtract

8

$8$ from

8

$8$ .

0

$0$

0

$0$

Step 1.3.4

Since

2

$2$ is a known root, divide the polynomial by

x - 2

$x - 2$ to find the quotient polynomial. This polynomial can then be used to find the remaining roots.

\frac{x^{4} - 4 x - 8}{x - 2}

$\frac{x^{4} - 4 x - 8}{x - 2}$

Step 1.3.5

Divide

x^{4} - 4 x - 8

$x^{4} - 4 x - 8$ by

x - 2

$x - 2$ .

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Step 1.3.5.1

Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of

0

$0$ .

x

$x$

2

$2$

x^{4}

$x^{4}$

0 x^{3}

$0 x^{3}$

0 x^{2}

$0 x^{2}$

4 x

$4 x$

8

$8$

Step 1.3.5.2

Divide the highest order term in the dividend

x^{4}

$x^{4}$ by the highest order term in divisor

x

$x$ .

x^{3}

$x^{3}$

x

$x$

2

$2$

x^{4}

$x^{4}$

0 x^{3}

$0 x^{3}$

0 x^{2}

$0 x^{2}$

4 x

$4 x$

8

$8$

Step 1.3.5.3

Multiply the new quotient term by the divisor.

x^{3}

$x^{3}$

x

$x$

2

$2$

x^{4}

$x^{4}$

0 x^{3}

$0 x^{3}$

0 x^{2}

$0 x^{2}$

4 x

$4 x$

8

$8$

x^{4}

$x^{4}$

2 x^{3}

$2 x^{3}$

Step 1.3.5.4

The expression needs to be subtracted from the dividend, so change all the signs in

x^{4} - 2 x^{3}

$x^{4} - 2 x^{3}$

x^{3}

$x^{3}$

x

$x$

2

$2$

x^{4}

$x^{4}$

0 x^{3}

$0 x^{3}$

0 x^{2}

$0 x^{2}$

4 x

$4 x$

8

$8$

x^{4}

$x^{4}$

2 x^{3}

$2 x^{3}$

Step 1.3.5.5

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

x^{3}

$x^{3}$

x

$x$

2

$2$

x^{4}

$x^{4}$

0 x^{3}

$0 x^{3}$

0 x^{2}

$0 x^{2}$

4 x

$4 x$

8

$8$

x^{4}

$x^{4}$

2 x^{3}

$2 x^{3}$

2 x^{3}

$2 x^{3}$

Step 1.3.5.6

Pull the next terms from the original dividend down into the current dividend.

x^{3}

$x^{3}$

x

$x$

2

$2$

x^{4}

$x^{4}$

0 x^{3}

$0 x^{3}$

0 x^{2}

$0 x^{2}$

4 x

$4 x$

8

$8$

x^{4}

$x^{4}$

2 x^{3}

$2 x^{3}$

2 x^{3}

$2 x^{3}$

0 x^{2}

$0 x^{2}$

Step 1.3.5.7

Divide the highest order term in the dividend

2 x^{3}

$2 x^{3}$ by the highest order term in divisor

x

$x$ .

x^{3}

$x^{3}$

2 x^{2}

$2 x^{2}$

x

$x$

2

$2$

x^{4}

$x^{4}$

0 x^{3}

$0 x^{3}$

0 x^{2}

$0 x^{2}$

4 x

$4 x$

8

$8$

x^{4}

$x^{4}$

2 x^{3}

$2 x^{3}$

2 x^{3}

$2 x^{3}$

0 x^{2}

$0 x^{2}$

Step 1.3.5.8

Multiply the new quotient term by the divisor.

x^{3}

$x^{3}$

2 x^{2}

$2 x^{2}$

x

$x$

2

$2$

x^{4}

$x^{4}$

0 x^{3}

$0 x^{3}$

0 x^{2}

$0 x^{2}$

4 x

$4 x$

8

$8$

x^{4}

$x^{4}$

2 x^{3}

$2 x^{3}$

2 x^{3}

$2 x^{3}$

0 x^{2}

$0 x^{2}$

2 x^{3}

$2 x^{3}$

4 x^{2}

$4 x^{2}$

Step 1.3.5.9

The expression needs to be subtracted from the dividend, so change all the signs in

2 x^{3} - 4 x^{2}

$2 x^{3} - 4 x^{2}$

x^{3}

$x^{3}$

2 x^{2}

$2 x^{2}$

x

$x$

2

$2$

x^{4}

$x^{4}$

0 x^{3}

$0 x^{3}$

0 x^{2}

$0 x^{2}$

4 x

$4 x$

8

$8$

x^{4}

$x^{4}$

2 x^{3}

$2 x^{3}$

2 x^{3}

$2 x^{3}$

0 x^{2}

$0 x^{2}$

2 x^{3}

$2 x^{3}$

4 x^{2}

$4 x^{2}$

Step 1.3.5.10

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

x^{3}

$x^{3}$

2 x^{2}

$2 x^{2}$

x

$x$

2

$2$

x^{4}

$x^{4}$

0 x^{3}

$0 x^{3}$

0 x^{2}

$0 x^{2}$

4 x

$4 x$

8

$8$

x^{4}

$x^{4}$

2 x^{3}

$2 x^{3}$

2 x^{3}

$2 x^{3}$

0 x^{2}

$0 x^{2}$

2 x^{3}

$2 x^{3}$

4 x^{2}

$4 x^{2}$

4 x^{2}

$4 x^{2}$

Step 1.3.5.11

Pull the next terms from the original dividend down into the current dividend.

x^{3}

$x^{3}$

2 x^{2}

$2 x^{2}$

x

$x$

2

$2$

x^{4}

$x^{4}$

0 x^{3}

$0 x^{3}$

0 x^{2}

$0 x^{2}$

4 x

$4 x$

8

$8$

x^{4}

$x^{4}$

2 x^{3}

$2 x^{3}$

2 x^{3}

$2 x^{3}$

0 x^{2}

$0 x^{2}$

2 x^{3}

$2 x^{3}$

4 x^{2}

$4 x^{2}$

4 x^{2}

$4 x^{2}$

4 x

$4 x$

Step 1.3.5.12

Divide the highest order term in the dividend

4 x^{2}

$4 x^{2}$ by the highest order term in divisor

x

$x$ .

x^{3}

$x^{3}$

2 x^{2}

$2 x^{2}$

4 x

$4 x$

x

$x$

2

$2$

x^{4}

$x^{4}$

0 x^{3}

$0 x^{3}$

0 x^{2}

$0 x^{2}$

4 x

$4 x$

8

$8$

x^{4}

$x^{4}$

2 x^{3}

$2 x^{3}$

2 x^{3}

$2 x^{3}$

0 x^{2}

$0 x^{2}$

2 x^{3}

$2 x^{3}$

4 x^{2}

$4 x^{2}$

4 x^{2}

$4 x^{2}$

4 x

$4 x$

Step 1.3.5.13

Multiply the new quotient term by the divisor.

x^{3}

$x^{3}$

2 x^{2}

$2 x^{2}$

4 x

$4 x$

x

$x$

2

$2$

x^{4}

$x^{4}$

0 x^{3}

$0 x^{3}$

0 x^{2}

$0 x^{2}$

4 x

$4 x$

8

$8$

x^{4}

$x^{4}$

2 x^{3}

$2 x^{3}$

2 x^{3}

$2 x^{3}$

0 x^{2}

$0 x^{2}$

2 x^{3}

$2 x^{3}$

4 x^{2}

$4 x^{2}$

4 x^{2}

$4 x^{2}$

4 x

$4 x$

4 x^{2}

$4 x^{2}$

8 x

$8 x$

Step 1.3.5.14

The expression needs to be subtracted from the dividend, so change all the signs in

4 x^{2} - 8 x

$4 x^{2} - 8 x$

x^{3}

$x^{3}$

2 x^{2}

$2 x^{2}$

4 x

$4 x$

x

$x$

2

$2$

x^{4}

$x^{4}$

0 x^{3}

$0 x^{3}$

0 x^{2}

$0 x^{2}$

4 x

$4 x$

8

$8$

x^{4}

$x^{4}$

2 x^{3}

$2 x^{3}$

2 x^{3}

$2 x^{3}$

0 x^{2}

$0 x^{2}$

2 x^{3}

$2 x^{3}$

4 x^{2}

$4 x^{2}$

4 x^{2}

$4 x^{2}$

4 x

$4 x$

4 x^{2}

$4 x^{2}$

8 x

$8 x$

Step 1.3.5.15

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

x^{3}

$x^{3}$

2 x^{2}

$2 x^{2}$

4 x

$4 x$

x

$x$

2

$2$

x^{4}

$x^{4}$

0 x^{3}

$0 x^{3}$

0 x^{2}

$0 x^{2}$

4 x

$4 x$

8

$8$

x^{4}

$x^{4}$

2 x^{3}

$2 x^{3}$

2 x^{3}

$2 x^{3}$

0 x^{2}

$0 x^{2}$

2 x^{3}

$2 x^{3}$

4 x^{2}

$4 x^{2}$

4 x^{2}

$4 x^{2}$

4 x

$4 x$

4 x^{2}

$4 x^{2}$

8 x

$8 x$

4 x

$4 x$

Step 1.3.5.16

Pull the next terms from the original dividend down into the current dividend.

x^{3}

$x^{3}$

2 x^{2}

$2 x^{2}$

4 x

$4 x$

x

$x$

2

$2$

x^{4}

$x^{4}$

0 x^{3}

$0 x^{3}$

0 x^{2}

$0 x^{2}$

4 x

$4 x$

8

$8$

x^{4}

$x^{4}$

2 x^{3}

$2 x^{3}$

2 x^{3}

$2 x^{3}$

0 x^{2}

$0 x^{2}$

2 x^{3}

$2 x^{3}$

4 x^{2}

$4 x^{2}$

4 x^{2}

$4 x^{2}$

4 x

$4 x$

4 x^{2}

$4 x^{2}$

8 x

$8 x$

4 x

$4 x$

8

$8$

Step 1.3.5.17

Divide the highest order term in the dividend

4 x

$4 x$ by the highest order term in divisor

x

$x$ .

x^{3}

$x^{3}$

2 x^{2}

$2 x^{2}$

4 x

$4 x$

4

$4$

x

$x$

2

$2$

x^{4}

$x^{4}$

0 x^{3}

$0 x^{3}$

0 x^{2}

$0 x^{2}$

4 x

$4 x$

8

$8$

x^{4}

$x^{4}$

2 x^{3}

$2 x^{3}$

2 x^{3}

$2 x^{3}$

0 x^{2}

$0 x^{2}$

2 x^{3}

$2 x^{3}$

4 x^{2}

$4 x^{2}$

4 x^{2}

$4 x^{2}$

4 x

$4 x$

4 x^{2}

$4 x^{2}$

8 x

$8 x$

4 x

$4 x$

8

$8$

Step 1.3.5.18

Multiply the new quotient term by the divisor.

x^{3}

$x^{3}$

2 x^{2}

$2 x^{2}$

4 x

$4 x$

4

$4$

x

$x$

2

$2$

x^{4}

$x^{4}$

0 x^{3}

$0 x^{3}$

0 x^{2}

$0 x^{2}$

4 x

$4 x$

8

$8$

x^{4}

$x^{4}$

2 x^{3}

$2 x^{3}$

2 x^{3}

$2 x^{3}$

0 x^{2}

$0 x^{2}$

2 x^{3}

$2 x^{3}$

4 x^{2}

$4 x^{2}$

4 x^{2}

$4 x^{2}$

4 x

$4 x$

4 x^{2}

$4 x^{2}$

8 x

$8 x$

4 x

$4 x$

8

$8$

4 x

$4 x$

8

$8$

Step 1.3.5.19

The expression needs to be subtracted from the dividend, so change all the signs in

4 x - 8

$4 x - 8$

x^{3}

$x^{3}$

2 x^{2}

$2 x^{2}$

4 x

$4 x$

4

$4$

x

$x$

2

$2$

x^{4}

$x^{4}$

0 x^{3}

$0 x^{3}$

0 x^{2}

$0 x^{2}$

4 x

$4 x$

8

$8$

x^{4}

$x^{4}$

2 x^{3}

$2 x^{3}$

2 x^{3}

$2 x^{3}$

0 x^{2}

$0 x^{2}$

2 x^{3}

$2 x^{3}$

4 x^{2}

$4 x^{2}$

4 x^{2}

$4 x^{2}$

4 x

$4 x$

4 x^{2}

$4 x^{2}$

8 x

$8 x$

4 x

$4 x$

8

$8$

4 x

$4 x$

8

$8$

Step 1.3.5.20

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

x^{3}

$x^{3}$

2 x^{2}

$2 x^{2}$

4 x

$4 x$

4

$4$

x

$x$

2

$2$

x^{4}

$x^{4}$

0 x^{3}

$0 x^{3}$

0 x^{2}

$0 x^{2}$

4 x

$4 x$

8

$8$

x^{4}

$x^{4}$

2 x^{3}

$2 x^{3}$

2 x^{3}

$2 x^{3}$

0 x^{2}

$0 x^{2}$

2 x^{3}

$2 x^{3}$

4 x^{2}

$4 x^{2}$

4 x^{2}

$4 x^{2}$

4 x

$4 x$

4 x^{2}

$4 x^{2}$

8 x

$8 x$

4 x

$4 x$

8

$8$

4 x

$4 x$

8

$8$

0

$0$

Step 1.3.5.21

Since the remander is

0

$0$ , the final answer is the quotient.

x^{3} + 2 x^{2} + 4 x + 4

$x^{3} + 2 x^{2} + 4 x + 4$

x^{3} + 2 x^{2} + 4 x + 4

$x^{3} + 2 x^{2} + 4 x + 4$

Step 1.3.6

Write

x^{4} - 4 x - 8

$x^{4} - 4 x - 8$ as a set of factors.

- x^{2} (x - 2) + (x - 2) (x^{3} + 2 x^{2} + 4 x + 4) = 0

$- x^{2} (x - 2) + (x - 2) (x^{3} + 2 x^{2} + 4 x + 4) = 0$

- x^{2} (x - 2) + (x - 2) (x^{3} + 2 x^{2} + 4 x + 4) = 0

$- x^{2} (x - 2) + (x - 2) (x^{3} + 2 x^{2} + 4 x + 4) = 0$

Step 1.4

Factor

x - 2

$x - 2$ out of

- x^{2} (x - 2) + (x - 2) (x^{3} + 2 x^{2} + 4 x + 4)

$- x^{2} (x - 2) + (x - 2) (x^{3} + 2 x^{2} + 4 x + 4)$ .

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Step 1.4.1

Factor

x - 2

$x - 2$ out of

- x^{2} (x - 2)

$- x^{2} (x - 2)$ .

(x - 2) (- x^{2}) + (x - 2) (x^{3} + 2 x^{2} + 4 x + 4) = 0

$(x - 2) (- x^{2}) + (x - 2) (x^{3} + 2 x^{2} + 4 x + 4) = 0$

Step 1.4.2

Factor

x - 2

$x - 2$ out of

(x - 2) (- x^{2}) + (x - 2) (x^{3} + 2 x^{2} + 4 x + 4)

$(x - 2) (- x^{2}) + (x - 2) (x^{3} + 2 x^{2} + 4 x + 4)$ .

(x - 2) (- x^{2} + x^{3} + 2 x^{2} + 4 x + 4) = 0

$(x - 2) (- x^{2} + x^{3} + 2 x^{2} + 4 x + 4) = 0$

(x - 2) (- x^{2} + x^{3} + 2 x^{2} + 4 x + 4) = 0

$(x - 2) (- x^{2} + x^{3} + 2 x^{2} + 4 x + 4) = 0$

Step 1.5

Add

- x^{2}

$- x^{2}$ and

2 x^{2}

$2 x^{2}$ .

(x - 2) (x^{3} + x^{2} + 4 x + 4) = 0

$(x - 2) (x^{3} + x^{2} + 4 x + 4) = 0$

Step 1.6

Factor.

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Step 1.6.1

Rewrite

x^{3} + x^{2} + 4 x + 4

$x^{3} + x^{2} + 4 x + 4$ in a factored form.

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Step 1.6.1.1

Factor out the greatest common factor from each group.

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Step 1.6.1.1.1

Group the first two terms and the last two terms.

(x - 2) ((x^{3} + x^{2}) + 4 x + 4) = 0

$(x - 2) ((x^{3} + x^{2}) + 4 x + 4) = 0$

Step 1.6.1.1.2

Factor out the greatest common factor (GCF) from each group.

(x - 2) (x^{2} (x + 1) + 4 (x + 1)) = 0

$(x - 2) (x^{2} (x + 1) + 4 (x + 1)) = 0$

(x - 2) (x^{2} (x + 1) + 4 (x + 1)) = 0

$(x - 2) (x^{2} (x + 1) + 4 (x + 1)) = 0$

Step 1.6.1.2

Factor the polynomial by factoring out the greatest common factor,

x + 1

$x + 1$ .

(x - 2) ((x + 1) (x^{2} + 4)) = 0

$(x - 2) ((x + 1) (x^{2} + 4)) = 0$

(x - 2) ((x + 1) (x^{2} + 4)) = 0

$(x - 2) ((x + 1) (x^{2} + 4)) = 0$

Step 1.6.2

Remove unnecessary parentheses.

(x - 2) (x + 1) (x^{2} + 4) = 0

$(x - 2) (x + 1) (x^{2} + 4) = 0$

(x - 2) (x + 1) (x^{2} + 4) = 0

$(x - 2) (x + 1) (x^{2} + 4) = 0$

(x - 2) (x + 1) (x^{2} + 4) = 0

$(x - 2) (x + 1) (x^{2} + 4) = 0$

Step 2

If any individual factor on the left side of the equation is equal to

0

$0$ , the entire expression will be equal to

0

$0$ .

x - 2 = 0

$x - 2 = 0$

x + 1 = 0

$x + 1 = 0$

x^{2} + 4 = 0

$x^{2} + 4 = 0$

Step 3

Set

x - 2

$x - 2$ equal to

0

$0$ and solve for

x

$x$ .

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Step 3.1

Set

x - 2

$x - 2$ equal to

0

$0$ .

x - 2 = 0

$x - 2 = 0$

Step 3.2

Add

2

$2$ to both sides of the equation.

x = 2

$x = 2$

x = 2

$x = 2$

Step 4

Set

x + 1

$x + 1$ equal to

0

$0$ and solve for

x

$x$ .

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Step 4.1

Set

x + 1

$x + 1$ equal to

0

$0$ .

x + 1 = 0

$x + 1 = 0$

Step 4.2

Subtract

1

$1$ from both sides of the equation.

x = - 1

$x = - 1$

x = - 1

$x = - 1$

Step 5

Set

x^{2} + 4

$x^{2} + 4$ equal to

0

$0$ and solve for

x

$x$ .

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Step 5.1

Set

x^{2} + 4

$x^{2} + 4$ equal to

0

$0$ .

x^{2} + 4 = 0

$x^{2} + 4 = 0$

Step 5.2

Solve

x^{2} + 4 = 0

$x^{2} + 4 = 0$ for

x

$x$ .

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Step 5.2.1

Subtract

4

$4$ from both sides of the equation.

x^{2} = - 4

$x^{2} = - 4$

Step 5.2.2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

x = \pm \sqrt{- 4}

$x = \pm \sqrt{- 4}$

Step 5.2.3

Simplify

\pm \sqrt{- 4}

$\pm \sqrt{- 4}$ .

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Step 5.2.3.1

Rewrite

- 4

$- 4$ as

- 1 (4)

$- 1 (4)$ .

x = \pm \sqrt{- 1 (4)}

$x = \pm \sqrt{- 1 (4)}$

Step 5.2.3.2

Rewrite

\sqrt{- 1 (4)}

$\sqrt{- 1 (4)}$ as

\sqrt{- 1} \cdot \sqrt{4}

$\sqrt{- 1} \cdot \sqrt{4}$ .

x = \pm \sqrt{- 1} \cdot \sqrt{4}

$x = \pm \sqrt{- 1} \cdot \sqrt{4}$

Step 5.2.3.3

Rewrite

\sqrt{- 1}

$\sqrt{- 1}$ as

i

$i$ .

x = \pm i \cdot \sqrt{4}

$x = \pm i \cdot \sqrt{4}$

Step 5.2.3.4

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

x = \pm i \cdot \sqrt{2^{2}}

$x = \pm i \cdot \sqrt{2^{2}}$

Step 5.2.3.5

Pull terms out from under the radical, assuming positive real numbers.

x = \pm i \cdot 2

$x = \pm i \cdot 2$

Step 5.2.3.6

Move

2

$2$ to the left of

i

$i$ .

x = \pm 2 i

$x = \pm 2 i$

x = \pm 2 i

$x = \pm 2 i$

Step 5.2.4

The complete solution is the result of both the positive and negative portions of the solution.

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Step 5.2.4.1

First, use the positive value of the

\pm

$\pm$ to find the first solution.

x = 2 i

$x = 2 i$

Step 5.2.4.2

Next, use the negative value of the

\pm

$\pm$ to find the second solution.

x = - 2 i

$x = - 2 i$

Step 5.2.4.3

The complete solution is the result of both the positive and negative portions of the solution.

x = 2 i, - 2 i

$x = 2 i, - 2 i$

x = 2 i, - 2 i

$x = 2 i, - 2 i$

x = 2 i, - 2 i

$x = 2 i, - 2 i$

x = 2 i, - 2 i

$x = 2 i, - 2 i$

Step 6

The final solution is all the values that make

(x - 2) (x + 1) (x^{2} + 4) = 0

$(x - 2) (x + 1) (x^{2} + 4) = 0$ true.

x = 2, - 1, 2 i, - 2 i

$x = 2, - 1, 2 i, - 2 i$