Solve 3x^2+44=7x^2-82

$$3 x ^ { 2 } + 44 = 7 x ^ { 2 } - 82$$

Solve for x

$$x = \frac{3 \sqrt{14}}{2} \approx 5.61248608$$

$$x = -\frac{3 \sqrt{14}}{2} \approx -5.61248608$$

Steps by Finding Square Root

Subtract 7x^{2} from both sides.

$$3x^{2}+44-7x^{2}=-82$$

Combine 3x^{2} and -7x^{2} to get -4x^{2}.

$$-4x^{2}+44=-82$$

Subtract 44 from both sides.

$$-4x^{2}=-82-44$$

Subtract 44 from -82 to get -126.

$$-4x^{2}=-126$$

Divide both sides by -4.

$$x^{2}=\frac{-126}{-4}$$

Reduce the fraction \frac{-126}{-4} to lowest terms by extracting and canceling out -2.

$$x^{2}=\frac{63}{2}$$

Take the square root of both sides of the equation.

$$x=\frac{3\sqrt{14}}{2} x=-\frac{3\sqrt{14}}{2}$$

Steps Using the Quadratic Formula

Subtract 7x^{2} from both sides.

$$3x^{2}+44-7x^{2}=-82$$

Combine 3x^{2} and -7x^{2} to get -4x^{2}.

$$-4x^{2}+44=-82$$

Add 82 to both sides.

$$-4x^{2}+44+82=0$$

Add 44 and 82 to get 126.

$$-4x^{2}+126=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -4 for a, 0 for b, and 126 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-4\right)\times 126}}{2\left(-4\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-4\right)\times 126}}{2\left(-4\right)}$$

Multiply -4 times -4.

$$x=\frac{0±\sqrt{16\times 126}}{2\left(-4\right)}$$

Multiply 16 times 126.

$$x=\frac{0±\sqrt{2016}}{2\left(-4\right)}$$

Take the square root of 2016.

$$x=\frac{0±12\sqrt{14}}{2\left(-4\right)}$$

Multiply 2 times -4.

$$x=\frac{0±12\sqrt{14}}{-8}$$

Now solve the equation x=\frac{0±12\sqrt{14}}{-8} when ± is plus.

$$x=-\frac{3\sqrt{14}}{2}$$

Now solve the equation x=\frac{0±12\sqrt{14}}{-8} when ± is minus.

$$x=\frac{3\sqrt{14}}{2}$$

The equation is now solved.

$$x=-\frac{3\sqrt{14}}{2} x=\frac{3\sqrt{14}}{2}$$