Solve x^2=-1sqrt{12^2-4(1)(-32)}

$${ x }^{ 2 } =-1 \sqrt{ { 12 }^{ 2 } -4(1)(-32) }$$

Solve for x (complex solution)

$$x=-\sqrt[4]{17}\times \left(2i\right)\approx -0-4.06108637i$$

$$x=\sqrt[4]{17}\times \left(2i\right)\approx 4.06108637i$$

Steps by Finding Square Root

Calculate 12 to the power of 2 and get 144.

$$x^{2}=-\sqrt{144-4\left(-32\right)}$$

Multiply 4 and -32 to get -128.

$$x^{2}=-\sqrt{144-\left(-128\right)}$$

The opposite of -128 is 128.

$$x^{2}=-\sqrt{144+128}$$

Add 144 and 128 to get 272.

$$x^{2}=-\sqrt{272}$$

Factor 272=4^{2}\times 17. Rewrite the square root of the product \sqrt{4^{2}\times 17} as the product of square roots \sqrt{4^{2}}\sqrt{17}. Take the square root of 4^{2}.

$$x^{2}=-4\sqrt{17}$$

The equation is now solved.

$$x=\sqrt[4]{17}\times \left(2i\right) x=-\sqrt[4]{17}\times \left(2i\right)$$

Steps Using the Quadratic Formula

Calculate 12 to the power of 2 and get 144.

$$x^{2}=-\sqrt{144-4\left(-32\right)}$$

Multiply 4 and -32 to get -128.

$$x^{2}=-\sqrt{144-\left(-128\right)}$$

The opposite of -128 is 128.

$$x^{2}=-\sqrt{144+128}$$

Add 144 and 128 to get 272.

$$x^{2}=-\sqrt{272}$$

Factor 272=4^{2}\times 17. Rewrite the square root of the product \sqrt{4^{2}\times 17} as the product of square roots \sqrt{4^{2}}\sqrt{17}. Take the square root of 4^{2}.

$$x^{2}=-4\sqrt{17}$$

Add 4\sqrt{17} to both sides.

$$x^{2}+4\sqrt{17}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 4\sqrt{17} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\sqrt{17}}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 4\sqrt{17}}}{2}$$

Multiply -4 times 4\sqrt{17}.

$$x=\frac{0±\sqrt{-16\sqrt{17}}}{2}$$

Take the square root of -16\sqrt{17}.

$$x=\frac{0±\sqrt[4]{17}\times \left(4i\right)}{2}$$

Now solve the equation x=\frac{0±\sqrt[4]{17}\times \left(4i\right)}{2} when ± is plus.

$$x=\sqrt[4]{17}\times \left(2i\right)$$

Now solve the equation x=\frac{0±\sqrt[4]{17}\times \left(4i\right)}{2} when ± is minus.

$$x=-\sqrt[4]{17}\times \left(2i\right)$$

The equation is now solved.

$$x=\sqrt[4]{17}\times \left(2i\right) x=-\sqrt[4]{17}\times \left(2i\right)$$