Solve 225x^2-360+194=0

$$225 x ^ { 2 } - 360 + 194 = 0$$

Solve for x

$$x=\frac{\sqrt{166}}{15}\approx 0.858939915$$

$$x=-\frac{\sqrt{166}}{15}\approx -0.858939915$$

Steps by Finding Square Root

Add -360 and 194 to get -166.

$$225x^{2}-166=0$$

Add 166 to both sides. Anything plus zero gives itself.

$$225x^{2}=166$$

Divide both sides by 225.

$$x^{2}=\frac{166}{225}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{166}}{15} x=-\frac{\sqrt{166}}{15}$$

Steps Using the Quadratic Formula

Add -360 and 194 to get -166.

$$225x^{2}-166=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 225 for a, 0 for b, and -166 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 225\left(-166\right)}}{2\times 225}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 225\left(-166\right)}}{2\times 225}$$

Multiply -4 times 225.

$$x=\frac{0±\sqrt{-900\left(-166\right)}}{2\times 225}$$

Multiply -900 times -166.

$$x=\frac{0±\sqrt{149400}}{2\times 225}$$

Take the square root of 149400.

$$x=\frac{0±30\sqrt{166}}{2\times 225}$$

Multiply 2 times 225.

$$x=\frac{0±30\sqrt{166}}{450}$$

Now solve the equation x=\frac{0±30\sqrt{166}}{450} when ± is plus.

$$x=\frac{\sqrt{166}}{15}$$

Now solve the equation x=\frac{0±30\sqrt{166}}{450} when ± is minus.

$$x=-\frac{\sqrt{166}}{15}$$

The equation is now solved.

$$x=\frac{\sqrt{166}}{15} x=-\frac{\sqrt{166}}{15}$$