Solve 24-x^2+4=0

$$24 - x ^ { 2 } + 4 = 0$$

Solve for x

$$x=2\sqrt{7}\approx 5.291502622$$

$$x=-2\sqrt{7}\approx -5.291502622$$

Steps by Finding Square Root

Add 24 and 4 to get 28.

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

Subtract 28 from both sides. Anything subtracted from zero gives its negation.

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

Divide both sides by -1.

$$x^{2}=\frac{-28}{-1}$$

Fraction \frac{-28}{-1} can be simplified to 28 by removing the negative sign from both the numerator and the denominator.

$$x^{2}=28$$

Take the square root of both sides of the equation.

$$x=2\sqrt{7} x=-2\sqrt{7}$$

Steps Using the Quadratic Formula

Add 24 and 4 to get 28.

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

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.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and 28 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 28}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times 28}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\times 28}}{2\left(-1\right)}$$

Multiply 4 times 28.

$$x=\frac{0±\sqrt{112}}{2\left(-1\right)}$$

Take the square root of 112.

$$x=\frac{0±4\sqrt{7}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±4\sqrt{7}}{-2}$$

Now solve the equation x=\frac{0±4\sqrt{7}}{-2} when ± is plus.

$$x=-2\sqrt{7}$$

Now solve the equation x=\frac{0±4\sqrt{7}}{-2} when ± is minus.

$$x=2\sqrt{7}$$

The equation is now solved.

$$x=-2\sqrt{7} x=2\sqrt{7}$$