Solve 4x^2-29+7=0

$$4 { x }^{ 2 } -29+7=0$$

Solve for x

$$x = \frac{\sqrt{22}}{2} \approx 2.34520788$$

$$x = -\frac{\sqrt{22}}{2} \approx -2.34520788$$

Steps by Finding Square Root

Add -29 and 7 to get -22.

$$4x^{2}-22=0$$

Add 22 to both sides. Anything plus zero gives itself.

$$4x^{2}=22$$

Divide both sides by 4.

$$x^{2}=\frac{22}{4}$$

Reduce the fraction \frac{22}{4} to lowest terms by extracting and canceling out 2.

$$x^{2}=\frac{11}{2}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{22}}{2} x=-\frac{\sqrt{22}}{2}$$

Steps Using the Quadratic Formula

Add -29 and 7 to get -22.

$$4x^{2}-22=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -22 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-22\right)}}{2\times 4}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 4\left(-22\right)}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16\left(-22\right)}}{2\times 4}$$

Multiply -16 times -22.

$$x=\frac{0±\sqrt{352}}{2\times 4}$$

Take the square root of 352.

$$x=\frac{0±4\sqrt{22}}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{0±4\sqrt{22}}{8}$$

Now solve the equation x=\frac{0±4\sqrt{22}}{8} when ± is plus.

$$x=\frac{\sqrt{22}}{2}$$

Now solve the equation x=\frac{0±4\sqrt{22}}{8} when ± is minus.

$$x=-\frac{\sqrt{22}}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{22}}{2} x=-\frac{\sqrt{22}}{2}$$