Solve 5x^2=6x^2-7

$$5 x ^ { 2 } = 6 x ^ { 2 } - 7$$

Solve for x

$$x=\sqrt{7}\approx 2.645751311$$

$$x=-\sqrt{7}\approx -2.645751311$$

Steps by Finding Square Root

Subtract 6x^{2} from both sides.

$$5x^{2}-6x^{2}=-7$$

Combine 5x^{2} and -6x^{2} to get -x^{2}.

$$-x^{2}=-7$$

Divide both sides by -1.

$$x^{2}=\frac{-7}{-1}$$

Fraction \frac{-7}{-1} can be simplified to 7 by removing the negative sign from both the numerator and the denominator.

$$x^{2}=7$$

Take the square root of both sides of the equation.

$$x=\sqrt{7} x=-\sqrt{7}$$

Steps Using the Quadratic Formula

Subtract 6x^{2} from both sides.

$$5x^{2}-6x^{2}=-7$$

Combine 5x^{2} and -6x^{2} to get -x^{2}.

$$-x^{2}=-7$$

Add 7 to both sides.

$$-x^{2}+7=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and 7 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 7}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times 7}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\times 7}}{2\left(-1\right)}$$

Multiply 4 times 7.

$$x=\frac{0±\sqrt{28}}{2\left(-1\right)}$$

Take the square root of 28.

$$x=\frac{0±2\sqrt{7}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±2\sqrt{7}}{-2}$$

Now solve the equation x=\frac{0±2\sqrt{7}}{-2} when ± is plus.

$$x=-\sqrt{7}$$

Now solve the equation x=\frac{0±2\sqrt{7}}{-2} when ± is minus.

$$x=\sqrt{7}$$

The equation is now solved.

$$x=-\sqrt{7} x=\sqrt{7}$$