Solve 25x^2+30+9=0

$$25 { x }^{ 2 } +30+9=0$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{39}i}{5}\approx -0-1.2489996i$$

$$x=\frac{\sqrt{39}i}{5}\approx 1.2489996i$$

Steps by Finding Square Root

Add 30 and 9 to get 39.

$$25x^{2}+39=0$$

Subtract 39 from both sides. Anything subtracted from zero gives its negation.

$$25x^{2}=-39$$

Divide both sides by 25.

$$x^{2}=-\frac{39}{25}$$

The equation is now solved.

$$x=\frac{\sqrt{39}i}{5} x=-\frac{\sqrt{39}i}{5}$$

Steps Using the Quadratic Formula

Add 30 and 9 to get 39.

$$25x^{2}+39=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 25 for a, 0 for b, and 39 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 25\times 39}}{2\times 25}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 25\times 39}}{2\times 25}$$

Multiply -4 times 25.

$$x=\frac{0±\sqrt{-100\times 39}}{2\times 25}$$

Multiply -100 times 39.

$$x=\frac{0±\sqrt{-3900}}{2\times 25}$$

Take the square root of -3900.

$$x=\frac{0±10\sqrt{39}i}{2\times 25}$$

Multiply 2 times 25.

$$x=\frac{0±10\sqrt{39}i}{50}$$

Now solve the equation x=\frac{0±10\sqrt{39}i}{50} when ± is plus.

$$x=\frac{\sqrt{39}i}{5}$$

Now solve the equation x=\frac{0±10\sqrt{39}i}{50} when ± is minus.

$$x=-\frac{\sqrt{39}i}{5}$$

The equation is now solved.

$$x=\frac{\sqrt{39}i}{5} x=-\frac{\sqrt{39}i}{5}$$