Solve x^2+25+57=0

$$x ^ { 2 } + 25 + 57 = 0$$

Solve for x (complex solution)

$$x=-\sqrt{82}i\approx -0-9.055385138i$$

$$x=\sqrt{82}i\approx 9.055385138i$$

Steps by Finding Square Root

Add 25 and 57 to get 82.

$$x^{2}+82=0$$

Subtract 82 from both sides. Anything subtracted from zero gives its negation.

$$x^{2}=-82$$

The equation is now solved.

$$x=\sqrt{82}i x=-\sqrt{82}i$$

Steps Using the Quadratic Formula

Add 25 and 57 to get 82.

$$x^{2}+82=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 82 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 82}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 82}}{2}$$

Multiply -4 times 82.

$$x=\frac{0±\sqrt{-328}}{2}$$

Take the square root of -328.

$$x=\frac{0±2\sqrt{82}i}{2}$$

Now solve the equation x=\frac{0±2\sqrt{82}i}{2} when ± is plus.

$$x=\sqrt{82}i$$

Now solve the equation x=\frac{0±2\sqrt{82}i}{2} when ± is minus.

$$x=-\sqrt{82}i$$

The equation is now solved.

$$x=\sqrt{82}i x=-\sqrt{82}i$$