Algebra Examples

$x^{2} + 9^{2} = 15^{2}$

Step 1

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

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Step 1.1

Simplify the left side.

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Step 1.1.1

Raise $9$ to the power of $2$ .

$x^{2} + 81 = 15^{2}$

Step 1.2

Simplify the right side.

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Step 1.2.1

Raise $15$ to the power of $2$ .

$x^{2} + 81 = 225$

Step 1.3

Subtract $225$ from both sides of the equation.

$x^{2} + 81 - 225 = 0$

Step 1.4

Subtract $225$ from $81$ .

$x^{2} - 144 = 0$

Step 2

Use the quadratic formula to find the solutions.

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

Step 3

Substitute the values $a = 1$ , $b = 0$ , and $c = - 144$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (1 \cdot - 144)}}{2 \cdot 1}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raising $0$ to any positive power yields $0$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 1 \cdot - 144}}{2 \cdot 1}$

Step 4.1.2

Multiply $- 4 \cdot 1 \cdot - 144$ .

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Step 4.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot - 144}}{2 \cdot 1}$

Step 4.1.2.2

Multiply $- 4$ by $- 144$ .

$x = \frac{0 \pm \sqrt{0 + 576}}{2 \cdot 1}$

Step 4.1.3

Add $0$ and $576$ .

$x = \frac{0 \pm \sqrt{576}}{2 \cdot 1}$

Step 4.1.4

Rewrite $576$ as $24^{2}$ .

$x = \frac{0 \pm \sqrt{24^{2}}}{2 \cdot 1}$

Step 4.1.5

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

$x = \frac{0 \pm 24}{2 \cdot 1}$

Step 4.2

Multiply $2$ by $1$ .

$x = \frac{0 \pm 24}{2}$

Step 4.3

Simplify $\frac{0 \pm 24}{2}$ .

$x = \pm 12$

Step 5

The final answer is the combination of both solutions.

$x = 12, - 12$