Solve x^2-20x^2+64=0

$$x ^ { 2 } - 20 x ^ { 2 } + 64 = 0$$

Solve for x

$$x = \frac{8 \sqrt{19}}{19} \approx 1.835325871$$

$$x = -\frac{8 \sqrt{19}}{19} \approx -1.835325871$$

Steps by Finding Square Root

Combine x^{2} and -20x^{2} to get -19x^{2}.

$$-19x^{2}+64=0$$

Subtract 64 from both sides. Anything subtracted from zero gives its negation.

$$-19x^{2}=-64$$

Divide both sides by -19.

$$x^{2}=\frac{-64}{-19}$$

Fraction \frac{-64}{-19} can be simplified to \frac{64}{19} by removing the negative sign from both the numerator and the denominator.

$$x^{2}=\frac{64}{19}$$

Take the square root of both sides of the equation.

$$x=\frac{8\sqrt{19}}{19} x=-\frac{8\sqrt{19}}{19}$$

Steps Using the Quadratic Formula

Combine x^{2} and -20x^{2} to get -19x^{2}.

$$-19x^{2}+64=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -19 for a, 0 for b, and 64 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-19\right)\times 64}}{2\left(-19\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-19\right)\times 64}}{2\left(-19\right)}$$

Multiply -4 times -19.

$$x=\frac{0±\sqrt{76\times 64}}{2\left(-19\right)}$$

Multiply 76 times 64.

$$x=\frac{0±\sqrt{4864}}{2\left(-19\right)}$$

Take the square root of 4864.

$$x=\frac{0±16\sqrt{19}}{2\left(-19\right)}$$

Multiply 2 times -19.

$$x=\frac{0±16\sqrt{19}}{-38}$$

Now solve the equation x=\frac{0±16\sqrt{19}}{-38} when ± is plus.

$$x=-\frac{8\sqrt{19}}{19}$$

Now solve the equation x=\frac{0±16\sqrt{19}}{-38} when ± is minus.

$$x=\frac{8\sqrt{19}}{19}$$

The equation is now solved.

$$x=-\frac{8\sqrt{19}}{19} x=\frac{8\sqrt{19}}{19}$$