Solve b^2+81=0

$$b ^ { 2 } + 81 = 0$$

Solve for b

$$b=-9i$$

$$b=9i$$

Steps by Finding Square Root

Subtract 81 from both sides. Anything subtracted from zero gives its negation.

$$b^{2}=-81$$

The equation is now solved.

$$b=9i b=-9i$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$b^{2}+81=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 81 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}-4\times 81}}{2}$$

Square 0.

$$b=\frac{0±\sqrt{-4\times 81}}{2}$$

Multiply -4 times 81.

$$b=\frac{0±\sqrt{-324}}{2}$$

Take the square root of -324.

$$b=\frac{0±18i}{2}$$

Now solve the equation b=\frac{0±18i}{2} when ± is plus.

$$b=9i$$

Now solve the equation b=\frac{0±18i}{2} when ± is minus.

$$b=-9i$$

The equation is now solved.

$$b=9i b=-9i$$