Solve 2.25=-1/5x^2+3.5

$$2.25 = - \frac { 1 } { 5 } x ^ { 2 } + 3.5$$

Solve for x

$$x=2.5$$

$$x=-2.5$$

Steps by Finding Square Root

Swap sides so that all variable terms are on the left hand side.

$$-\frac{1}{5}x^{2}+3.5=2.25$$

Subtract 3.5 from both sides.

$$-\frac{1}{5}x^{2}=2.25-3.5$$

Subtract 3.5 from 2.25 to get -1.25.

$$-\frac{1}{5}x^{2}=-1.25$$

Multiply both sides by -5, the reciprocal of -\frac{1}{5}.

$$x^{2}=-1.25\left(-5\right)$$

Multiply -1.25 and -5 to get 6.25.

$$x^{2}=6.25$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Swap sides so that all variable terms are on the left hand side.

$$-\frac{1}{5}x^{2}+3.5=2.25$$

Subtract 2.25 from both sides.

$$-\frac{1}{5}x^{2}+3.5-2.25=0$$

Subtract 2.25 from 3.5 to get 1.25.

$$-\frac{1}{5}x^{2}+1.25=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -\frac{1}{5} for a, 0 for b, and 1.25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{1}{5}\right)\times 1.25}}{2\left(-\frac{1}{5}\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{1}{5}\right)\times 1.25}}{2\left(-\frac{1}{5}\right)}$$

Multiply -4 times -\frac{1}{5}.

$$x=\frac{0±\sqrt{\frac{4}{5}\times 1.25}}{2\left(-\frac{1}{5}\right)}$$

Multiply \frac{4}{5} times 1.25 by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$x=\frac{0±\sqrt{1}}{2\left(-\frac{1}{5}\right)}$$

Take the square root of 1.

$$x=\frac{0±1}{2\left(-\frac{1}{5}\right)}$$

Multiply 2 times -\frac{1}{5}.

$$x=\frac{0±1}{-\frac{2}{5}}$$

Now solve the equation x=\frac{0±1}{-\frac{2}{5}} when ± is plus. Divide 1 by -\frac{2}{5} by multiplying 1 by the reciprocal of -\frac{2}{5}.

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

Now solve the equation x=\frac{0±1}{-\frac{2}{5}} when ± is minus. Divide -1 by -\frac{2}{5} by multiplying -1 by the reciprocal of -\frac{2}{5}.

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

The equation is now solved.

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