Solve 4x^2-5=0

$$4 x ^ { 2 } - 5 = 0$$

Solve for x

$$x = \frac{\sqrt{5}}{2} \approx 1.118033989$$

$$x = -\frac{\sqrt{5}}{2} \approx -1.118033989$$

Steps by Finding Square Root

Add 5 to both sides. Anything plus zero gives itself.

$$4x^{2}=5$$

Divide both sides by 4.

$$x^{2}=\frac{5}{4}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{5}}{2} x=-\frac{\sqrt{5}}{2}$$

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.

$$4x^{2}-5=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -5 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-5\right)}}{2\times 4}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 4\left(-5\right)}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16\left(-5\right)}}{2\times 4}$$

Multiply -16 times -5.

$$x=\frac{0±\sqrt{80}}{2\times 4}$$

Take the square root of 80.

$$x=\frac{0±4\sqrt{5}}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{0±4\sqrt{5}}{8}$$

Now solve the equation x=\frac{0±4\sqrt{5}}{8} when ± is plus.

$$x=\frac{\sqrt{5}}{2}$$

Now solve the equation x=\frac{0±4\sqrt{5}}{8} when ± is minus.

$$x=-\frac{\sqrt{5}}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{5}}{2} x=-\frac{\sqrt{5}}{2}$$