Solve 1.5x^2-4=11

$$1.5 x ^ { 2 } - 4 = 11$$

Solve for x

$$x=\sqrt{10}\approx 3.16227766$$

$$x=-\sqrt{10}\approx -3.16227766$$

Steps by Finding Square Root

Add 4 to both sides.

$$1.5x^{2}=11+4$$

Add 11 and 4 to get 15.

$$1.5x^{2}=15$$

Divide both sides by 1.5.

$$x^{2}=\frac{15}{1.5}$$

Expand \frac{15}{1.5} by multiplying both numerator and the denominator by 10.

$$x^{2}=\frac{150}{15}$$

Divide 150 by 15 to get 10.

$$x^{2}=10$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Subtract 11 from both sides.

$$1.5x^{2}-4-11=0$$

Subtract 11 from -4 to get -15.

$$1.5x^{2}-15=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1.5 for a, 0 for b, and -15 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 1.5\left(-15\right)}}{2\times 1.5}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 1.5\left(-15\right)}}{2\times 1.5}$$

Multiply -4 times 1.5.

$$x=\frac{0±\sqrt{-6\left(-15\right)}}{2\times 1.5}$$

Multiply -6 times -15.

$$x=\frac{0±\sqrt{90}}{2\times 1.5}$$

Take the square root of 90.

$$x=\frac{0±3\sqrt{10}}{2\times 1.5}$$

Multiply 2 times 1.5.

$$x=\frac{0±3\sqrt{10}}{3}$$

Now solve the equation x=\frac{0±3\sqrt{10}}{3} when ± is plus.

$$x=\sqrt{10}$$

Now solve the equation x=\frac{0±3\sqrt{10}}{3} when ± is minus.

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

The equation is now solved.

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