Solve 3.05=-0.2x^2+3.5

$$3.05 = - 0.2 x ^ { 2 } + 3.5$$

Solve for x

$$x=1.5$$

$$x=-1.5$$

Steps by Finding Square Root

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

$$-0.2x^{2}+3.5=3.05$$

Subtract 3.5 from both sides.

$$-0.2x^{2}=3.05-3.5$$

Subtract 3.5 from 3.05 to get -0.45.

$$-0.2x^{2}=-0.45$$

Divide both sides by -0.2.

$$x^{2}=\frac{-0.45}{-0.2}$$

Expand \frac{-0.45}{-0.2} by multiplying both numerator and the denominator by 100.

$$x^{2}=\frac{-45}{-20}$$

Reduce the fraction \frac{-45}{-20} to lowest terms by extracting and canceling out -5.

$$x^{2}=\frac{9}{4}$$

Take the square root of both sides of the equation.

$$x=\frac{3}{2} x=-\frac{3}{2}$$

Steps Using the Quadratic Formula

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

$$-0.2x^{2}+3.5=3.05$$

Subtract 3.05 from both sides.

$$-0.2x^{2}+3.5-3.05=0$$

Subtract 3.05 from 3.5 to get 0.45.

$$-0.2x^{2}+0.45=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -0.2 for a, 0 for b, and 0.45 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-0.2\right)\times 0.45}}{2\left(-0.2\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-0.2\right)\times 0.45}}{2\left(-0.2\right)}$$

Multiply -4 times -0.2.

$$x=\frac{0±\sqrt{0.8\times 0.45}}{2\left(-0.2\right)}$$

Multiply 0.8 times 0.45 by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$x=\frac{0±\sqrt{0.36}}{2\left(-0.2\right)}$$

Take the square root of 0.36.

$$x=\frac{0±\frac{3}{5}}{2\left(-0.2\right)}$$

Multiply 2 times -0.2.

$$x=\frac{0±\frac{3}{5}}{-0.4}$$

Now solve the equation x=\frac{0±\frac{3}{5}}{-0.4} when ± is plus.

$$x=-\frac{3}{2}$$

Now solve the equation x=\frac{0±\frac{3}{5}}{-0.4} when ± is minus.

$$x=\frac{3}{2}$$

The equation is now solved.

$$x=-\frac{3}{2} x=\frac{3}{2}$$