Solve Using the Quadratic Formula 10x^2-56=88-6x^2

$10 x^{2} - 56 = 88 - 6 x^{2}$

Step 1

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

Move all the expressions to the left side of the equation.

Subtract $88$ from both sides of the equation.

$10 x^{2} - 56 - 88 = - 6 x^{2}$

Add $6 x^{2}$ to both sides of the equation.

$10 x^{2} - 56 - 88 + 6 x^{2} = 0$

Simplify $10 x^{2} - 56 - 88 + 6 x^{2}$ .

Add $10 x^{2}$ and $6 x^{2}$ .

$16 x^{2} - 56 - 88 = 0$

Subtract $88$ from $- 56$ .

$16 x^{2} - 144 = 0$

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 $a = 16$ , $b = 0$ , and $c = - 144$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (16 \cdot - 144)}}{2 \cdot 16}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 16 \cdot - 144}}{2 \cdot 16}$

Multiply $- 4 \cdot 16 \cdot - 144$ .

Multiply $- 4$ by $16$ .

$x = \frac{0 \pm \sqrt{0 - 64 \cdot - 144}}{2 \cdot 16}$

Multiply $- 64$ by $- 144$ .

$x = \frac{0 \pm \sqrt{0 + 9216}}{2 \cdot 16}$

Add $0$ and $9216$ .

$x = \frac{0 \pm \sqrt{9216}}{2 \cdot 16}$

Rewrite $9216$ as $96^{2}$ .

$x = \frac{0 \pm \sqrt{96^{2}}}{2 \cdot 16}$

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

$x = \frac{0 \pm 96}{2 \cdot 16}$

Multiply $2$ by $16$ .

$x = \frac{0 \pm 96}{32}$

Simplify $\frac{0 \pm 96}{32}$ .

$x = \pm 3$

Step 5

The final answer is the combination of both solutions.

$x = 3, - 3$