Solve x^2=20.25

$${ x }^{ 2 } =20.25$$

Solve for x

$$x=4.5$$

$$x=-4.5$$

Steps Using Difference of Squares

Subtract 20.25 from both sides.

$$x^{2}-20.25=0$$

Consider x^{2}-20.25. Rewrite x^{2}-20.25 as x^{2}-\left(\frac{9}{2}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-\frac{9}{2}\right)\left(x+\frac{9}{2}\right)=0$$

To find equation solutions, solve x-\frac{9}{2}=0 and x+\frac{9}{2}=0.

$$x=\frac{9}{2} x=-\frac{9}{2}$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x=\frac{9}{2} x=-\frac{9}{2}$$

Steps Using the Quadratic Formula

Subtract 20.25 from both sides.

$$x^{2}-20.25=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -20.25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-20.25\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-20.25\right)}}{2}$$

Multiply -4 times -20.25.

$$x=\frac{0±\sqrt{81}}{2}$$

Take the square root of 81.

$$x=\frac{0±9}{2}$$

Now solve the equation x=\frac{0±9}{2} when ± is plus. Divide 9 by 2.

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

Now solve the equation x=\frac{0±9}{2} when ± is minus. Divide -9 by 2.

$$x=-\frac{9}{2}$$

The equation is now solved.

$$x=\frac{9}{2} x=-\frac{9}{2}$$