Solve 4x^2+5=40

$$4 x ^ { 2 } + 5 = 40$$

Solve for x

$$x = \frac{\sqrt{35}}{2} \approx 2.958039892$$

$$x = -\frac{\sqrt{35}}{2} \approx -2.958039892$$

Steps by Finding Square Root

Subtract 5 from both sides.

$$4x^{2}=40-5$$

Subtract 5 from 40 to get 35.

$$4x^{2}=35$$

Divide both sides by 4.

$$x^{2}=\frac{35}{4}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{35}}{2} x=-\frac{\sqrt{35}}{2}$$

Steps Using the Quadratic Formula

Subtract 40 from both sides.

$$4x^{2}+5-40=0$$

Subtract 40 from 5 to get -35.

$$4x^{2}-35=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -35 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-35\right)}}{2\times 4}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 4\left(-35\right)}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16\left(-35\right)}}{2\times 4}$$

Multiply -16 times -35.

$$x=\frac{0±\sqrt{560}}{2\times 4}$$

Take the square root of 560.

$$x=\frac{0±4\sqrt{35}}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{0±4\sqrt{35}}{8}$$

Now solve the equation x=\frac{0±4\sqrt{35}}{8} when ± is plus.

$$x=\frac{\sqrt{35}}{2}$$

Now solve the equation x=\frac{0±4\sqrt{35}}{8} when ± is minus.

$$x=-\frac{\sqrt{35}}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{35}}{2} x=-\frac{\sqrt{35}}{2}$$