Solve 0.18x^2+0.017-300=0

$$0.18 { x }^{ 2 } +0.017-300=0$$

Solve for x

$$x = \frac{\sqrt{1499915}}{30} \approx 40.823672327$$

$$x = -\frac{\sqrt{1499915}}{30} \approx -40.823672327$$

Steps by Finding Square Root

Subtract 300 from 0.017 to get -299.983.

$$0.18x^{2}-299.983=0$$

Add 299.983 to both sides. Anything plus zero gives itself.

$$0.18x^{2}=299.983$$

Divide both sides by 0.18.

$$x^{2}=\frac{299.983}{0.18}$$

Expand \frac{299.983}{0.18} by multiplying both numerator and the denominator by 1000.

$$x^{2}=\frac{299983}{180}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{1499915}}{30} x=-\frac{\sqrt{1499915}}{30}$$

Steps Using the Quadratic Formula

Subtract 300 from 0.017 to get -299.983.

$$0.18x^{2}-299.983=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 0.18 for a, 0 for b, and -299.983 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 0.18\left(-299.983\right)}}{2\times 0.18}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 0.18\left(-299.983\right)}}{2\times 0.18}$$

Multiply -4 times 0.18.

$$x=\frac{0±\sqrt{-0.72\left(-299.983\right)}}{2\times 0.18}$$

Multiply -0.72 times -299.983 by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$x=\frac{0±\sqrt{215.98776}}{2\times 0.18}$$

Take the square root of 215.98776.

$$x=\frac{0±\frac{3\sqrt{1499915}}{250}}{2\times 0.18}$$

Multiply 2 times 0.18.

$$x=\frac{0±\frac{3\sqrt{1499915}}{250}}{0.36}$$

Now solve the equation x=\frac{0±\frac{3\sqrt{1499915}}{250}}{0.36} when ± is plus.

$$x=\frac{\sqrt{1499915}}{30}$$

Now solve the equation x=\frac{0±\frac{3\sqrt{1499915}}{250}}{0.36} when ± is minus.

$$x=-\frac{\sqrt{1499915}}{30}$$

The equation is now solved.

$$x=\frac{\sqrt{1499915}}{30} x=-\frac{\sqrt{1499915}}{30}$$