Algebra Examples

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

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

Step 1

Move all terms to the left side of the equation and simplify.

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Step 1.1

Subtract

10

$10$ from both sides of the equation.

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

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

Step 1.2

Subtract

10

$10$ from

- 6

$- 6$ .

x^{2} + 6 x - 16 = 0

$x^{2} + 6 x - 16 = 0$

x^{2} + 6 x - 16 = 0

$x^{2} + 6 x - 16 = 0$

Step 2

Use the quadratic formula to find the solutions.

\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values

a = 1

$a = 1$ ,

b = 6

$b = 6$ , and

c = - 16

$c = - 16$ into the quadratic formula and solve for

x

$x$ .

\frac{- 6 \pm \sqrt{6^{2} - 4 \cdot (1 \cdot - 16)}}{2 \cdot 1}

$\frac{- 6 \pm \sqrt{6^{2} - 4 \cdot (1 \cdot - 16)}}{2 \cdot 1}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise

6

$6$ to the power of

2

$2$ .

x = \frac{- 6 \pm \sqrt{36 - 4 \cdot 1 \cdot - 16}}{2 \cdot 1}

$x = \frac{- 6 \pm \sqrt{36 - 4 \cdot 1 \cdot - 16}}{2 \cdot 1}$

Step 4.1.2

Multiply

- 4 \cdot 1 \cdot - 16

$- 4 \cdot 1 \cdot - 16$ .

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Step 4.1.2.1

Multiply

- 4

$- 4$ by

1

$1$ .

x = \frac{- 6 \pm \sqrt{36 - 4 \cdot - 16}}{2 \cdot 1}

$x = \frac{- 6 \pm \sqrt{36 - 4 \cdot - 16}}{2 \cdot 1}$

Step 4.1.2.2

Multiply

- 4

$- 4$ by

- 16

$- 16$ .

x = \frac{- 6 \pm \sqrt{36 + 64}}{2 \cdot 1}

$x = \frac{- 6 \pm \sqrt{36 + 64}}{2 \cdot 1}$

x = \frac{- 6 \pm \sqrt{36 + 64}}{2 \cdot 1}

$x = \frac{- 6 \pm \sqrt{36 + 64}}{2 \cdot 1}$

Step 4.1.3

Add

36

$36$ and

64

$64$ .

x = \frac{- 6 \pm \sqrt{100}}{2 \cdot 1}

$x = \frac{- 6 \pm \sqrt{100}}{2 \cdot 1}$

Step 4.1.4

Rewrite

100

$100$ as

10^{2}

$10^{2}$ .

x = \frac{- 6 \pm \sqrt{10^{2}}}{2 \cdot 1}

$x = \frac{- 6 \pm \sqrt{10^{2}}}{2 \cdot 1}$

Step 4.1.5

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

x = \frac{- 6 \pm 10}{2 \cdot 1}

$x = \frac{- 6 \pm 10}{2 \cdot 1}$

x = \frac{- 6 \pm 10}{2 \cdot 1}

$x = \frac{- 6 \pm 10}{2 \cdot 1}$

Step 4.2

Multiply

2

$2$ by

1

$1$ .

x = \frac{- 6 \pm 10}{2}

$x = \frac{- 6 \pm 10}{2}$

Step 4.3

Simplify

\frac{- 6 \pm 10}{2}

$\frac{- 6 \pm 10}{2}$ .

x = - 3 \pm 5

$x = - 3 \pm 5$

x = - 3 \pm 5

$x = - 3 \pm 5$

Step 5

The final answer is the combination of both solutions.

x = 2, - 8

$x = 2, - 8$