Solve Using the Quadratic Formula 5^2+7^2=c^2

$5^{2} + 7^{2} = c^{2}$

Step 1

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

Simplify the left side.

Simplify $5^{2} + 7^{2}$ .

Simplify each term.

Raise $5$ to the power of $2$ .

$25 + 7^{2} = c^{2}$

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

$25 + 49 = c^{2}$

Add $25$ and $49$ .

$74 = c^{2}$

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

$74 - c^{2} = 0$

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 $c = 74$ into the quadratic formula and solve for $c$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (- 1 \cdot 74)}}{2 \cdot - 1}$

Step 4

Simplify.

Simplify the numerator.

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

$c = \frac{0 \pm \sqrt{0 - 4 \cdot - 1 \cdot 74}}{2 \cdot - 1}$

Multiply $- 4 \cdot - 1 \cdot 74$ .

Multiply $- 4$ by $- 1$ .

$c = \frac{0 \pm \sqrt{0 + 4 \cdot 74}}{2 \cdot - 1}$

Multiply $4$ by $74$ .

$c = \frac{0 \pm \sqrt{0 + 296}}{2 \cdot - 1}$

Add $0$ and $296$ .

$c = \frac{0 \pm \sqrt{296}}{2 \cdot - 1}$

Rewrite $296$ as $2^{2} \cdot 74$ .

Factor $4$ out of $296$ .

$c = \frac{0 \pm \sqrt{4 (74)}}{2 \cdot - 1}$

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

$c = \frac{0 \pm \sqrt{2^{2} \cdot 74}}{2 \cdot - 1}$

Pull terms out from under the radical.

$c = \frac{0 \pm 2 \sqrt{74}}{2 \cdot - 1}$

Multiply $2$ by $- 1$ .

$c = \frac{0 \pm 2 \sqrt{74}}{- 2}$

Simplify $\frac{0 \pm 2 \sqrt{74}}{- 2}$ .

$c = \pm \sqrt{74}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$c = \pm \sqrt{74}$

Decimal Form:

$c = 8.60232526 \dots, - 8.60232526 \dots$

Solve Using the Quadratic Formula 5^2+7^2=c^2

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