Solve 6.25-x^2=0

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

Solve for x

$$x=2.5$$

$$x=-2.5$$

Steps by Finding Square Root

Subtract 6.25 from both sides. Anything subtracted from zero gives its negation.

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

Divide both sides by -1.

$$x^{2}=\frac{-6.25}{-1}$$

Expand \frac{-6.25}{-1} by multiplying both numerator and the denominator by 100.

$$x^{2}=\frac{-625}{-100}$$

Reduce the fraction \frac{-625}{-100} to lowest terms by extracting and canceling out -25.

$$x^{2}=\frac{25}{4}$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

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

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}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 6.25}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times 6.25}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\times 6.25}}{2\left(-1\right)}$$

Multiply 4 times 6.25.

$$x=\frac{0±\sqrt{25}}{2\left(-1\right)}$$

Take the square root of 25.

$$x=\frac{0±5}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±5}{-2}$$

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.

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