Solve -4x^2+1=0

$$-4 { x }^{ 2 } +1=0$$

Solve for x

$$x=\frac{1}{2}=0.5$$

$$x=-\frac{1}{2}=-0.5$$

Steps by Finding Square Root

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$-4x^{2}=-1$$

Divide both sides by -4.

$$x^{2}=\frac{-1}{-4}$$

Fraction \frac{-1}{-4} can be simplified to \frac{1}{4} by removing the negative sign from both the numerator and the denominator.

$$x^{2}=\frac{1}{4}$$

Take the square root of both sides of the equation.

$$x=\frac{1}{2} x=-\frac{1}{2}$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-4x^{2}+1=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -4 for a, 0 for b, and 1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Square 0.

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

Multiply -4 times -4.

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

Take the square root of 16.

$$x=\frac{0±4}{2\left(-4\right)}$$

Multiply 2 times -4.

$$x=\frac{0±4}{-8}$$

Now solve the equation x=\frac{0±4}{-8} when ± is plus. Reduce the fraction \frac{4}{-8} to lowest terms by extracting and canceling out 4.

$$x=-\frac{1}{2}$$

Now solve the equation x=\frac{0±4}{-8} when ± is minus. Reduce the fraction \frac{-4}{-8} to lowest terms by extracting and canceling out 4.

$$x=\frac{1}{2}$$

The equation is now solved.

$$x=-\frac{1}{2} x=\frac{1}{2}$$