Solve 1.5x*x=300

$$1.5 x \times x = 300$$

Solve for x

$$x=10\sqrt{2}\approx 14.142135624$$

$$x=-10\sqrt{2}\approx -14.142135624$$

Steps by Finding Square Root

Multiply x and x to get x^{2}.

$$1.5x^{2}=300$$

Divide both sides by 1.5.

$$x^{2}=\frac{300}{1.5}$$

Expand \frac{300}{1.5} by multiplying both numerator and the denominator by 10.

$$x^{2}=\frac{3000}{15}$$

Divide 3000 by 15 to get 200.

$$x^{2}=200$$

Take the square root of both sides of the equation.

$$x=10\sqrt{2} x=-10\sqrt{2}$$

Steps Using the Quadratic Formula

Multiply x and x to get x^{2}.

$$1.5x^{2}=300$$

Subtract 300 from both sides.

$$1.5x^{2}-300=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1.5 for a, 0 for b, and -300 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 1.5\left(-300\right)}}{2\times 1.5}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 1.5\left(-300\right)}}{2\times 1.5}$$

Multiply -4 times 1.5.

$$x=\frac{0±\sqrt{-6\left(-300\right)}}{2\times 1.5}$$

Multiply -6 times -300.

$$x=\frac{0±\sqrt{1800}}{2\times 1.5}$$

Take the square root of 1800.

$$x=\frac{0±30\sqrt{2}}{2\times 1.5}$$

Multiply 2 times 1.5.

$$x=\frac{0±30\sqrt{2}}{3}$$

Now solve the equation x=\frac{0±30\sqrt{2}}{3} when ± is plus.

$$x=10\sqrt{2}$$

Now solve the equation x=\frac{0±30\sqrt{2}}{3} when ± is minus.

$$x=-10\sqrt{2}$$

The equation is now solved.

$$x=10\sqrt{2} x=-10\sqrt{2}$$