Solve Using the Quadratic Formula 16x^2+10=131

$16 x^{2} + 10 = 131$

Step 1

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

Subtract $131$ from both sides of the equation.

$16 x^{2} + 10 - 131 = 0$

Subtract $131$ from $10$ .

$16 x^{2} - 121 = 0$

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 $a = 16$ , $b = 0$ , and $c = - 121$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (16 \cdot - 121)}}{2 \cdot 16}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 16 \cdot - 121}}{2 \cdot 16}$

Multiply $- 4 \cdot 16 \cdot - 121$ .

Multiply $- 4$ by $16$ .

$x = \frac{0 \pm \sqrt{0 - 64 \cdot - 121}}{2 \cdot 16}$

Multiply $- 64$ by $- 121$ .

$x = \frac{0 \pm \sqrt{0 + 7744}}{2 \cdot 16}$

Add $0$ and $7744$ .

$x = \frac{0 \pm \sqrt{7744}}{2 \cdot 16}$

Rewrite $7744$ as $88^{2}$ .

$x = \frac{0 \pm \sqrt{88^{2}}}{2 \cdot 16}$

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

$x = \frac{0 \pm 88}{2 \cdot 16}$

Multiply $2$ by $16$ .

$x = \frac{0 \pm 88}{32}$

Simplify $\frac{0 \pm 88}{32}$ .

$x = \frac{\pm 11}{4}$

Step 5

The final answer is the combination of both solutions.

$x = \frac{11}{4}, - \frac{11}{4}$