Solve 8x^2+7=5x^2+4

$$8 { x }^{ 2 } +7=5 { x }^{ 2 } +4$$

Solve for x (complex solution)

$$x=-i$$

$$x=i$$

Steps by Finding Square Root

Subtract 5x^{2} from both sides.

$$8x^{2}+7-5x^{2}=4$$

Combine 8x^{2} and -5x^{2} to get 3x^{2}.

$$3x^{2}+7=4$$

Subtract 7 from both sides.

$$3x^{2}=4-7$$

Subtract 7 from 4 to get -3.

$$3x^{2}=-3$$

Divide both sides by 3.

$$x^{2}=\frac{-3}{3}$$

Divide -3 by 3 to get -1.

$$x^{2}=-1$$

The equation is now solved.

$$x=i x=-i$$

Steps Using the Quadratic Formula

Subtract 5x^{2} from both sides.

$$8x^{2}+7-5x^{2}=4$$

Combine 8x^{2} and -5x^{2} to get 3x^{2}.

$$3x^{2}+7=4$$

Subtract 4 from both sides.

$$3x^{2}+7-4=0$$

Subtract 4 from 7 to get 3.

$$3x^{2}+3=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and 3 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\times 3}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\times 3}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\times 3}}{2\times 3}$$

Multiply -12 times 3.

$$x=\frac{0±\sqrt{-36}}{2\times 3}$$

Take the square root of -36.

$$x=\frac{0±6i}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±6i}{6}$$

Now solve the equation x=\frac{0±6i}{6} when ± is plus.

$$x=i$$

Now solve the equation x=\frac{0±6i}{6} when ± is minus.

$$x=-i$$

The equation is now solved.

$$x=i x=-i$$