Solve 2=4(x^2-7/4)

$$2=4( { x }^{ 2 } - \frac{ 7 }{ 4 } )$$

Solve for x

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

$$x = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

Steps Using Difference of Squares

Divide both sides by 4.

$$\frac{2}{4}=x^{2}-\frac{7}{4}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}=x^{2}-\frac{7}{4}$$

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

$$x^{2}-\frac{7}{4}=\frac{1}{2}$$

Subtract \frac{1}{2} from both sides.

$$x^{2}-\frac{7}{4}-\frac{1}{2}=0$$

Subtract \frac{1}{2} from -\frac{7}{4} to get -\frac{9}{4}.

$$x^{2}-\frac{9}{4}=0$$

Multiply both sides by 4.

$$4x^{2}-9=0$$

Consider 4x^{2}-9. Rewrite 4x^{2}-9 as \left(2x\right)^{2}-3^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(2x-3\right)\left(2x+3\right)=0$$

To find equation solutions, solve 2x-3=0 and 2x+3=0.

$$x=\frac{3}{2} x=-\frac{3}{2}$$

Steps by Finding Square Root

Divide both sides by 4.

$$\frac{2}{4}=x^{2}-\frac{7}{4}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}=x^{2}-\frac{7}{4}$$

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

$$x^{2}-\frac{7}{4}=\frac{1}{2}$$

Add \frac{7}{4} to both sides.

$$x^{2}=\frac{1}{2}+\frac{7}{4}$$

Add \frac{1}{2} and \frac{7}{4} to get \frac{9}{4}.

$$x^{2}=\frac{9}{4}$$

Take the square root of both sides of the equation.

$$x=\frac{3}{2} x=-\frac{3}{2}$$

Steps Using the Quadratic Formula

Divide both sides by 4.

$$\frac{2}{4}=x^{2}-\frac{7}{4}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}=x^{2}-\frac{7}{4}$$

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

$$x^{2}-\frac{7}{4}=\frac{1}{2}$$

Subtract \frac{1}{2} from both sides.

$$x^{2}-\frac{7}{4}-\frac{1}{2}=0$$

Subtract \frac{1}{2} from -\frac{7}{4} to get -\frac{9}{4}.

$$x^{2}-\frac{9}{4}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{9}{4} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{9}{4}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{9}{4}\right)}}{2}$$

Multiply -4 times -\frac{9}{4}.

$$x=\frac{0±\sqrt{9}}{2}$$

Take the square root of 9.

$$x=\frac{0±3}{2}$$

Now solve the equation x=\frac{0±3}{2} when ± is plus. Divide 3 by 2.

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

Now solve the equation x=\frac{0±3}{2} when ± is minus. Divide -3 by 2.

$$x=-\frac{3}{2}$$

The equation is now solved.

$$x=\frac{3}{2} x=-\frac{3}{2}$$