Solve a^2=(-2.5)^2

$$a ^ { 2 } = ( - 2.5 ) ^ { 2 }$$

Solve for a

$$a=2.5$$

$$a=-2.5$$

Steps Using Difference of Squares

Calculate -2.5 to the power of 2 and get 6.25.

$$a^{2}=6.25$$

Subtract 6.25 from both sides.

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

Consider a^{2}-6.25. Rewrite a^{2}-6.25 as a^{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).

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

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

$$a=2.5 a=-2.5$$

Steps by Finding Square Root

Calculate -2.5 to the power of 2 and get 6.25.

$$a^{2}=6.25$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Calculate -2.5 to the power of 2 and get 6.25.

$$a^{2}=6.25$$

Subtract 6.25 from both sides.

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

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}.

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

Square 0.

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

Multiply -4 times -6.25.

$$a=\frac{0±\sqrt{25}}{2}$$

Take the square root of 25.

$$a=\frac{0±5}{2}$$

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

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

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

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

The equation is now solved.

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