Solve x^2-16x^2+16=0

$${ x }^{ 2 } -16 { x }^{ 2 } +16 = 0$$

Solve for x

$$x = \frac{4 \sqrt{15}}{15} \approx 1.032795559$$

$$x = -\frac{4 \sqrt{15}}{15} \approx -1.032795559$$

Steps by Finding Square Root

Combine x^{2} and -16x^{2} to get -15x^{2}.

$$-15x^{2}+16=0$$

Subtract 16 from both sides. Anything subtracted from zero gives its negation.

$$-15x^{2}=-16$$

Divide both sides by -15.

$$x^{2}=\frac{-16}{-15}$$

Fraction \frac{-16}{-15} can be simplified to \frac{16}{15} by removing the negative sign from both the numerator and the denominator.

$$x^{2}=\frac{16}{15}$$

Take the square root of both sides of the equation.

$$x=\frac{4\sqrt{15}}{15} x=-\frac{4\sqrt{15}}{15}$$

Steps Using the Quadratic Formula

Combine x^{2} and -16x^{2} to get -15x^{2}.

$$-15x^{2}+16=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -15 for a, 0 for b, and 16 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-15\right)\times 16}}{2\left(-15\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-15\right)\times 16}}{2\left(-15\right)}$$

Multiply -4 times -15.

$$x=\frac{0±\sqrt{60\times 16}}{2\left(-15\right)}$$

Multiply 60 times 16.

$$x=\frac{0±\sqrt{960}}{2\left(-15\right)}$$

Take the square root of 960.

$$x=\frac{0±8\sqrt{15}}{2\left(-15\right)}$$

Multiply 2 times -15.

$$x=\frac{0±8\sqrt{15}}{-30}$$

Now solve the equation x=\frac{0±8\sqrt{15}}{-30} when ± is plus.

$$x=-\frac{4\sqrt{15}}{15}$$

Now solve the equation x=\frac{0±8\sqrt{15}}{-30} when ± is minus.

$$x=\frac{4\sqrt{15}}{15}$$

The equation is now solved.

$$x=-\frac{4\sqrt{15}}{15} x=\frac{4\sqrt{15}}{15}$$