Solve x^2=6.25

$${ x }^{ 2 } =6.25$$

Solve for x

$$x=2.5$$

$$x=-2.5$$

Steps Using Difference of Squares

Subtract 6.25 from both sides.

$$x^{2}-6.25=0$$

Consider x^{2}-6.25. Rewrite x^{2}-6.25 as x^{2}-\left(\frac{5}{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).

$$\left(x-\frac{5}{2}\right)\left(x+\frac{5}{2}\right)=0$$

To find equation solutions, solve x-\frac{5}{2}=0 and x+\frac{5}{2}=0.

$$x=\frac{5}{2} x=-\frac{5}{2}$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x=\frac{5}{2} x=-\frac{5}{2}$$

Steps Using the Quadratic Formula

Subtract 6.25 from both sides.

$$x^{2}-6.25=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -6.25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-6.25\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-6.25\right)}}{2}$$

Multiply -4 times -6.25.

$$x=\frac{0±\sqrt{25}}{2}$$

Take the square root of 25.

$$x=\frac{0±5}{2}$$

Now solve the equation x=\frac{0±5}{2} when ± is plus. Divide 5 by 2.

$$x=\frac{5}{2}$$

Now solve the equation x=\frac{0±5}{2} when ± is minus. Divide -5 by 2.

$$x=-\frac{5}{2}$$

The equation is now solved.

$$x=\frac{5}{2} x=-\frac{5}{2}$$