Solve x^2=5^2-4*8^2

$$x ^ { 2 } = 5 ^ { 2 } - 4 \cdot 8 ^ { 2 }$$

Solve for x (complex solution)

$$x=-\sqrt{231}i\approx -0-15.198684154i$$

$$x=\sqrt{231}i\approx 15.198684154i$$

Steps by Finding Square Root

Calculate 5 to the power of 2 and get 25.

$$x^{2}=25-4\times 8^{2}$$

Calculate 8 to the power of 2 and get 64.

$$x^{2}=25-4\times 64$$

Multiply 4 and 64 to get 256.

$$x^{2}=25-256$$

Subtract 256 from 25 to get -231.

$$x^{2}=-231$$

The equation is now solved.

$$x=\sqrt{231}i x=-\sqrt{231}i$$

Steps Using the Quadratic Formula

Calculate 5 to the power of 2 and get 25.

$$x^{2}=25-4\times 8^{2}$$

Calculate 8 to the power of 2 and get 64.

$$x^{2}=25-4\times 64$$

Multiply 4 and 64 to get 256.

$$x^{2}=25-256$$

Subtract 256 from 25 to get -231.

$$x^{2}=-231$$

Add 231 to both sides.

$$x^{2}+231=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 231 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 231}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 231}}{2}$$

Multiply -4 times 231.

$$x=\frac{0±\sqrt{-924}}{2}$$

Take the square root of -924.

$$x=\frac{0±2\sqrt{231}i}{2}$$

Now solve the equation x=\frac{0±2\sqrt{231}i}{2} when ± is plus.

$$x=\sqrt{231}i$$

Now solve the equation x=\frac{0±2\sqrt{231}i}{2} when ± is minus.

$$x=-\sqrt{231}i$$

The equation is now solved.

$$x=\sqrt{231}i x=-\sqrt{231}i$$