Solve 28x^2-46=0

$$28 x ^ { 2 } - 46 = 0$$

Solve for x

$$x = \frac{\sqrt{322}}{14} \approx 1.281739889$$

$$x = -\frac{\sqrt{322}}{14} \approx -1.281739889$$

Steps by Finding Square Root

Add 46 to both sides. Anything plus zero gives itself.

$$28x^{2}=46$$

Divide both sides by 28.

$$x^{2}=\frac{46}{28}$$

Reduce the fraction \frac{46}{28} to lowest terms by extracting and canceling out 2.

$$x^{2}=\frac{23}{14}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{322}}{14} x=-\frac{\sqrt{322}}{14}$$

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.

$$28x^{2}-46=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 28 for a, 0 for b, and -46 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 28\left(-46\right)}}{2\times 28}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 28\left(-46\right)}}{2\times 28}$$

Multiply -4 times 28.

$$x=\frac{0±\sqrt{-112\left(-46\right)}}{2\times 28}$$

Multiply -112 times -46.

$$x=\frac{0±\sqrt{5152}}{2\times 28}$$

Take the square root of 5152.

$$x=\frac{0±4\sqrt{322}}{2\times 28}$$

Multiply 2 times 28.

$$x=\frac{0±4\sqrt{322}}{56}$$

Now solve the equation x=\frac{0±4\sqrt{322}}{56} when ± is plus.

$$x=\frac{\sqrt{322}}{14}$$

Now solve the equation x=\frac{0±4\sqrt{322}}{56} when ± is minus.

$$x=-\frac{\sqrt{322}}{14}$$

The equation is now solved.

$$x=\frac{\sqrt{322}}{14} x=-\frac{\sqrt{322}}{14}$$