Solve x^2+(8sqrt{2}*1/2)^2=3^2

$$x ^ { 2 } + ( 8 \sqrt { 2 } \times \frac { 1 } { 2 } ) ^ { 2 } = 3 ^ { 2 }$$

Solve for x (complex solution)

$$x=-\sqrt{23}i\approx -0-4.795831523i$$

$$x=\sqrt{23}i\approx 4.795831523i$$

Steps by Finding Square Root

Multiply 8 and \frac{1}{2} to get 4.

$$x^{2}+\left(4\sqrt{2}\right)^{2}=3^{2}$$

Expand \left(4\sqrt{2}\right)^{2}.

$$x^{2}+4^{2}\left(\sqrt{2}\right)^{2}=3^{2}$$

Calculate 4 to the power of 2 and get 16.

$$x^{2}+16\left(\sqrt{2}\right)^{2}=3^{2}$$

The square of \sqrt{2} is 2.

$$x^{2}+16\times 2=3^{2}$$

Multiply 16 and 2 to get 32.

$$x^{2}+32=3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$x^{2}+32=9$$

Subtract 32 from both sides.

$$x^{2}=9-32$$

Subtract 32 from 9 to get -23.

$$x^{2}=-23$$

The equation is now solved.

$$x=\sqrt{23}i x=-\sqrt{23}i$$

Steps Using the Quadratic Formula

Multiply 8 and \frac{1}{2} to get 4.

$$x^{2}+\left(4\sqrt{2}\right)^{2}=3^{2}$$

Expand \left(4\sqrt{2}\right)^{2}.

$$x^{2}+4^{2}\left(\sqrt{2}\right)^{2}=3^{2}$$

Calculate 4 to the power of 2 and get 16.

$$x^{2}+16\left(\sqrt{2}\right)^{2}=3^{2}$$

The square of \sqrt{2} is 2.

$$x^{2}+16\times 2=3^{2}$$

Multiply 16 and 2 to get 32.

$$x^{2}+32=3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$x^{2}+32=9$$

Subtract 9 from both sides.

$$x^{2}+32-9=0$$

Subtract 9 from 32 to get 23.

$$x^{2}+23=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 23 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 23}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 23}}{2}$$

Multiply -4 times 23.

$$x=\frac{0±\sqrt{-92}}{2}$$

Take the square root of -92.

$$x=\frac{0±2\sqrt{23}i}{2}$$

Now solve the equation x=\frac{0±2\sqrt{23}i}{2} when ± is plus.

$$x=\sqrt{23}i$$

Now solve the equation x=\frac{0±2\sqrt{23}i}{2} when ± is minus.

$$x=-\sqrt{23}i$$

The equation is now solved.

$$x=\sqrt{23}i x=-\sqrt{23}i$$