Solve Using the Quadratic Formula 7^2+9^2=C^2

$7^{2} + 9^{2} = C^{2}$

Step 1

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

Simplify the left side.

Simplify $7^{2} + 9^{2}$ .

Simplify each term.

Raise $7$ to the power of $2$ .

$49 + 9^{2} = C^{2}$

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

$49 + 81 = C^{2}$

Add $49$ and $81$ .

$130 = C^{2}$

Subtract $C^{2}$ from both sides of the equation.

$130 - C^{2} = 0$

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 $c = 130$ into the quadratic formula and solve for $C$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (- 1 \cdot 130)}}{2 \cdot - 1}$

Step 4

Simplify.

Simplify the numerator.

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

$C = \frac{0 \pm \sqrt{0 - 4 \cdot - 1 \cdot 130}}{2 \cdot - 1}$

Multiply $- 4 \cdot - 1 \cdot 130$ .

Multiply $- 4$ by $- 1$ .

$C = \frac{0 \pm \sqrt{0 + 4 \cdot 130}}{2 \cdot - 1}$

Multiply $4$ by $130$ .

$C = \frac{0 \pm \sqrt{0 + 520}}{2 \cdot - 1}$

Add $0$ and $520$ .

$C = \frac{0 \pm \sqrt{520}}{2 \cdot - 1}$

Rewrite $520$ as $2^{2} \cdot 130$ .

Factor $4$ out of $520$ .

$C = \frac{0 \pm \sqrt{4 (130)}}{2 \cdot - 1}$

Rewrite $4$ as $2^{2}$ .

$C = \frac{0 \pm \sqrt{2^{2} \cdot 130}}{2 \cdot - 1}$

Pull terms out from under the radical.

$C = \frac{0 \pm 2 \sqrt{130}}{2 \cdot - 1}$

Multiply $2$ by $- 1$ .

$C = \frac{0 \pm 2 \sqrt{130}}{- 2}$

Simplify $\frac{0 \pm 2 \sqrt{130}}{- 2}$ .

$C = \pm \sqrt{130}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$C = \pm \sqrt{130}$

Decimal Form:

$C = 11.40175425 \dots, - 11.40175425 \dots$

Solve Using the Quadratic Formula 7^2+9^2=C^2

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