Solve 4*x^2-92=0

$$4 \cdot x ^ { 2 } - 92 = 0$$

Solve for x

$$x=\sqrt{23}\approx 4.795831523$$

$$x=-\sqrt{23}\approx -4.795831523$$

Steps by Finding Square Root

Add 92 to both sides. Anything plus zero gives itself.

$$4x^{2}=92$$

Divide both sides by 4.

$$x^{2}=\frac{92}{4}$$

Divide 92 by 4 to get 23.

$$x^{2}=23$$

Take the square root of both sides of the equation.

$$x=\sqrt{23} x=-\sqrt{23}$$

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.

$$4x^{2}-92=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -92 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-92\right)}}{2\times 4}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 4\left(-92\right)}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16\left(-92\right)}}{2\times 4}$$

Multiply -16 times -92.

$$x=\frac{0±\sqrt{1472}}{2\times 4}$$

Take the square root of 1472.

$$x=\frac{0±8\sqrt{23}}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{0±8\sqrt{23}}{8}$$

Now solve the equation x=\frac{0±8\sqrt{23}}{8} when ± is plus.

$$x=\sqrt{23}$$

Now solve the equation x=\frac{0±8\sqrt{23}}{8} when ± is minus.

$$x=-\sqrt{23}$$

The equation is now solved.

$$x=\sqrt{23} x=-\sqrt{23}$$