Solve 6x^2+7=1

$$6 x ^ { 2 } + 7 = 1$$

Solve for x (complex solution)

$$x=-i$$

$$x=i$$

Steps by Finding Square Root

Subtract 7 from both sides.

$$6x^{2}=1-7$$

Subtract 7 from 1 to get -6.

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

Divide both sides by 6.

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

Divide -6 by 6 to get -1.

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

The equation is now solved.

$$x=i x=-i$$

Steps Using the Quadratic Formula

Subtract 1 from both sides.

$$6x^{2}+7-1=0$$

Subtract 1 from 7 to get 6.

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

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

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

Square 0.

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

Multiply -4 times 6.

$$x=\frac{0±\sqrt{-24\times 6}}{2\times 6}$$

Multiply -24 times 6.

$$x=\frac{0±\sqrt{-144}}{2\times 6}$$

Take the square root of -144.

$$x=\frac{0±12i}{2\times 6}$$

Multiply 2 times 6.

$$x=\frac{0±12i}{12}$$

Now solve the equation x=\frac{0±12i}{12} when ± is plus.

$$x=i$$

Now solve the equation x=\frac{0±12i}{12} when ± is minus.

$$x=-i$$

The equation is now solved.

$$x=i x=-i$$