Algebra Examples

x^{2} + 6 x - 10 = 0

$x^{2} + 6 x - 10 = 0$

Step 1

Add

10

$10$ to both sides of the equation.

x^{2} + 6 x = 10

$x^{2} + 6 x = 10$

Step 2

To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of

b

$b$ .

{(\frac{b}{2})}^{2} = {(3)}^{2}

${(\frac{b}{2})}^{2} = {(3)}^{2}$

Step 3

Add the term to each side of the equation.

x^{2} + 6 x + {(3)}^{2} = 10 + {(3)}^{2}

$x^{2} + 6 x + {(3)}^{2} = 10 + {(3)}^{2}$

Step 4

Simplify the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Raise

3

$3$ to the power of

2

$2$ .

x^{2} + 6 x + 9 = 10 + {(3)}^{2}

$x^{2} + 6 x + 9 = 10 + {(3)}^{2}$

x^{2} + 6 x + 9 = 10 + {(3)}^{2}

$x^{2} + 6 x + 9 = 10 + {(3)}^{2}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify

10 + {(3)}^{2}

$10 + {(3)}^{2}$ .

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Step 4.2.1.1

Raise

3

$3$ to the power of

2

$2$ .

x^{2} + 6 x + 9 = 10 + 9

$x^{2} + 6 x + 9 = 10 + 9$

Step 4.2.1.2

Add

10

$10$ and

9

$9$ .

x^{2} + 6 x + 9 = 19

$x^{2} + 6 x + 9 = 19$

x^{2} + 6 x + 9 = 19

$x^{2} + 6 x + 9 = 19$

x^{2} + 6 x + 9 = 19

$x^{2} + 6 x + 9 = 19$

x^{2} + 6 x + 9 = 19

$x^{2} + 6 x + 9 = 19$

Step 5

Factor the perfect trinomial square into

{(x + 3)}^{2}

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

{(x + 3)}^{2} = 19

${(x + 3)}^{2} = 19$

Step 6

Solve the equation for

x

$x$ .

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Step 6.1

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

x + 3 = \pm \sqrt{19}

$x + 3 = \pm \sqrt{19}$

Step 6.2

Subtract

3

$3$ from both sides of the equation.

x = \pm \sqrt{19} - 3

$x = \pm \sqrt{19} - 3$

x = \pm \sqrt{19} - 3

$x = \pm \sqrt{19} - 3$

Step 7

The result can be shown in multiple forms.

Exact Form:

x = \pm \sqrt{19} - 3

$x = \pm \sqrt{19} - 3$

Decimal Form:

x = 1.35889894 \dots, - 7.35889894 \dots

$x = 1.35889894 \dots, - 7.35889894 \dots$