Solve 24=1/23x^2

$$24= \frac{ 1 }{ 2 } 3 { x }^{ 2 }$$

Solve for x

$$x=4$$

$$x=-4$$

Steps Using Difference of Squares

Multiply \frac{1}{2} and 3 to get \frac{3}{2}.

$$24=\frac{3}{2}x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{3}{2}x^{2}=24$$

Subtract 24 from both sides.

$$\frac{3}{2}x^{2}-24=0$$

Divide both sides by \frac{3}{2}.

$$x^{2}-16=0$$

Consider x^{2}-16. Rewrite x^{2}-16 as x^{2}-4^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-4\right)\left(x+4\right)=0$$

To find equation solutions, solve x-4=0 and x+4=0.

$$x=4 x=-4$$

Steps by Finding Square Root

Multiply \frac{1}{2} and 3 to get \frac{3}{2}.

$$24=\frac{3}{2}x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{3}{2}x^{2}=24$$

Multiply both sides by \frac{2}{3}, the reciprocal of \frac{3}{2}.

$$x^{2}=24\times \frac{2}{3}$$

Multiply 24 and \frac{2}{3} to get 16.

$$x^{2}=16$$

Take the square root of both sides of the equation.

$$x=4 x=-4$$

Steps Using the Quadratic Formula

Multiply \frac{1}{2} and 3 to get \frac{3}{2}.

$$24=\frac{3}{2}x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{3}{2}x^{2}=24$$

Subtract 24 from both sides.

$$\frac{3}{2}x^{2}-24=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{3}{2} for a, 0 for b, and -24 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{3}{2}\left(-24\right)}}{2\times \frac{3}{2}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{3}{2}\left(-24\right)}}{2\times \frac{3}{2}}$$

Multiply -4 times \frac{3}{2}.

$$x=\frac{0±\sqrt{-6\left(-24\right)}}{2\times \frac{3}{2}}$$

Multiply -6 times -24.

$$x=\frac{0±\sqrt{144}}{2\times \frac{3}{2}}$$

Take the square root of 144.

$$x=\frac{0±12}{2\times \frac{3}{2}}$$

Multiply 2 times \frac{3}{2}.

$$x=\frac{0±12}{3}$$

Now solve the equation x=\frac{0±12}{3} when ± is plus. Divide 12 by 3.

$$x=4$$

Now solve the equation x=\frac{0±12}{3} when ± is minus. Divide -12 by 3.

$$x=-4$$

The equation is now solved.

$$x=4 x=-4$$