Solve 4x^2+2+5=1

$$4 x ^ { 2 } + 2 + 5 = 1$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{6}i}{2}\approx -0-1.224744871i$$

$$x=\frac{\sqrt{6}i}{2}\approx 1.224744871i$$

Steps by Finding Square Root

Add 2 and 5 to get 7.

$$4x^{2}+7=1$$

Subtract 7 from both sides.

$$4x^{2}=1-7$$

Subtract 7 from 1 to get -6.

$$4x^{2}=-6$$

Divide both sides by 4.

$$x^{2}=\frac{-6}{4}$$

Reduce the fraction \frac{-6}{4} to lowest terms by extracting and canceling out 2.

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

The equation is now solved.

$$x=\frac{\sqrt{6}i}{2} x=-\frac{\sqrt{6}i}{2}$$

Steps Using the Quadratic Formula

Add 2 and 5 to get 7.

$$4x^{2}+7=1$$

Subtract 1 from both sides.

$$4x^{2}+7-1=0$$

Subtract 1 from 7 to get 6.

$$4x^{2}+6=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and 6 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\times 6}}{2\times 4}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 4\times 6}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16\times 6}}{2\times 4}$$

Multiply -16 times 6.

$$x=\frac{0±\sqrt{-96}}{2\times 4}$$

Take the square root of -96.

$$x=\frac{0±4\sqrt{6}i}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{0±4\sqrt{6}i}{8}$$

Now solve the equation x=\frac{0±4\sqrt{6}i}{8} when ± is plus.

$$x=\frac{\sqrt{6}i}{2}$$

Now solve the equation x=\frac{0±4\sqrt{6}i}{8} when ± is minus.

$$x=-\frac{\sqrt{6}i}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{6}i}{2} x=-\frac{\sqrt{6}i}{2}$$