Solve -7x^2-6=57

$$- 7 x ^ { 2 } - 6 = 57$$

Solve for x (complex solution)

$$x=-3i$$

$$x=3i$$

Steps by Finding Square Root

Add 6 to both sides.

$$-7x^{2}=57+6$$

Add 57 and 6 to get 63.

$$-7x^{2}=63$$

Divide both sides by -7.

$$x^{2}=\frac{63}{-7}$$

Divide 63 by -7 to get -9.

$$x^{2}=-9$$

The equation is now solved.

$$x=3i x=-3i$$

Steps Using the Quadratic Formula

Subtract 57 from both sides.

$$-7x^{2}-6-57=0$$

Subtract 57 from -6 to get -63.

$$-7x^{2}-63=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -7 for a, 0 for b, and -63 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-7\right)\left(-63\right)}}{2\left(-7\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-7\right)\left(-63\right)}}{2\left(-7\right)}$$

Multiply -4 times -7.

$$x=\frac{0±\sqrt{28\left(-63\right)}}{2\left(-7\right)}$$

Multiply 28 times -63.

$$x=\frac{0±\sqrt{-1764}}{2\left(-7\right)}$$

Take the square root of -1764.

$$x=\frac{0±42i}{2\left(-7\right)}$$

Multiply 2 times -7.

$$x=\frac{0±42i}{-14}$$

Now solve the equation x=\frac{0±42i}{-14} when ± is plus.

$$x=-3i$$

Now solve the equation x=\frac{0±42i}{-14} when ± is minus.

$$x=3i$$

The equation is now solved.

$$x=-3i x=3i$$