Solve 9x^2+10=-25

$$9 x ^ { 2 } + 10 = - 25$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{35}i}{3}\approx -0-1.972026594i$$

$$x=\frac{\sqrt{35}i}{3}\approx 1.972026594i$$

Steps by Finding Square Root

Subtract 10 from both sides.

$$9x^{2}=-25-10$$

Subtract 10 from -25 to get -35.

$$9x^{2}=-35$$

Divide both sides by 9.

$$x^{2}=-\frac{35}{9}$$

The equation is now solved.

$$x=\frac{\sqrt{35}i}{3} x=-\frac{\sqrt{35}i}{3}$$

Steps Using the Quadratic Formula

Add 25 to both sides.

$$9x^{2}+10+25=0$$

Add 10 and 25 to get 35.

$$9x^{2}+35=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 9 for a, 0 for b, and 35 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 9\times 35}}{2\times 9}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 9\times 35}}{2\times 9}$$

Multiply -4 times 9.

$$x=\frac{0±\sqrt{-36\times 35}}{2\times 9}$$

Multiply -36 times 35.

$$x=\frac{0±\sqrt{-1260}}{2\times 9}$$

Take the square root of -1260.

$$x=\frac{0±6\sqrt{35}i}{2\times 9}$$

Multiply 2 times 9.

$$x=\frac{0±6\sqrt{35}i}{18}$$

Now solve the equation x=\frac{0±6\sqrt{35}i}{18} when ± is plus.

$$x=\frac{\sqrt{35}i}{3}$$

Now solve the equation x=\frac{0±6\sqrt{35}i}{18} when ± is minus.

$$x=-\frac{\sqrt{35}i}{3}$$

The equation is now solved.

$$x=\frac{\sqrt{35}i}{3} x=-\frac{\sqrt{35}i}{3}$$