Solve 56-4x^2=0

$$56 - 4 x ^ { 2 } = 0$$

Solve for x

$$x=\sqrt{14}\approx 3.741657387$$

$$x=-\sqrt{14}\approx -3.741657387$$

Steps by Finding Square Root

Subtract 56 from both sides. Anything subtracted from zero gives its negation.

$$-4x^{2}=-56$$

Divide both sides by -4.

$$x^{2}=\frac{-56}{-4}$$

Divide -56 by -4 to get 14.

$$x^{2}=14$$

Take the square root of both sides of the equation.

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

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.

$$-4x^{2}+56=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -4 for a, 0 for b, and 56 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-4\right)\times 56}}{2\left(-4\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-4\right)\times 56}}{2\left(-4\right)}$$

Multiply -4 times -4.

$$x=\frac{0±\sqrt{16\times 56}}{2\left(-4\right)}$$

Multiply 16 times 56.

$$x=\frac{0±\sqrt{896}}{2\left(-4\right)}$$

Take the square root of 896.

$$x=\frac{0±8\sqrt{14}}{2\left(-4\right)}$$

Multiply 2 times -4.

$$x=\frac{0±8\sqrt{14}}{-8}$$

Now solve the equation x=\frac{0±8\sqrt{14}}{-8} when ± is plus.

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

Now solve the equation x=\frac{0±8\sqrt{14}}{-8} when ± is minus.

$$x=\sqrt{14}$$

The equation is now solved.

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