Solve x^2=729/4

$$x ^ { 2 } = \frac { 729 } { 4 }$$

Solve for x

$$x = \frac{27}{2} = 13\frac{1}{2} = 13.5$$

$$x = -\frac{27}{2} = -13\frac{1}{2} = -13.5$$

Steps Using Difference of Squares

Subtract \frac{729}{4} from both sides.

$$x^{2}-\frac{729}{4}=0$$

Multiply both sides by 4.

$$4x^{2}-729=0$$

Consider 4x^{2}-729. Rewrite 4x^{2}-729 as \left(2x\right)^{2}-27^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(2x-27\right)\left(2x+27\right)=0$$

To find equation solutions, solve 2x-27=0 and 2x+27=0.

$$x=\frac{27}{2} x=-\frac{27}{2}$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x=\frac{27}{2} x=-\frac{27}{2}$$

Steps Using the Quadratic Formula

Subtract \frac{729}{4} from both sides.

$$x^{2}-\frac{729}{4}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{729}{4} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{729}{4}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{729}{4}\right)}}{2}$$

Multiply -4 times -\frac{729}{4}.

$$x=\frac{0±\sqrt{729}}{2}$$

Take the square root of 729.

$$x=\frac{0±27}{2}$$

Now solve the equation x=\frac{0±27}{2} when ± is plus. Divide 27 by 2.

$$x=\frac{27}{2}$$

Now solve the equation x=\frac{0±27}{2} when ± is minus. Divide -27 by 2.

$$x=-\frac{27}{2}$$

The equation is now solved.

$$x=\frac{27}{2} x=-\frac{27}{2}$$