Solve 1^3/1^2=1.5^2/x^2

$$\frac{ { 1 }^{ 3 } }{ { 1 }^{ 2 } } = \frac{ { 1.5 }^{ 2 } }{ { x }^{ 2 } }$$

Solve for x

$$x=1.5$$

$$x=-1.5$$

Steps Using Difference of Squares

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x^{2}.

$$x^{2}\times 1^{3}=1.5^{2}$$

Calculate 1 to the power of 3 and get 1.

$$x^{2}\times 1=1.5^{2}$$

Calculate 1.5 to the power of 2 and get 2.25.

$$x^{2}\times 1=2.25$$

Subtract 2.25 from both sides.

$$x^{2}\times 1-2.25=0$$

Reorder the terms.

$$x^{2}-2.25=0$$

Consider x^{2}-2.25. Rewrite x^{2}-2.25 as x^{2}-\left(\frac{3}{2}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-\frac{3}{2}\right)\left(x+\frac{3}{2}\right)=0$$

To find equation solutions, solve x-\frac{3}{2}=0 and x+\frac{3}{2}=0.

$$x=\frac{3}{2} x=-1.5$$

Steps by Finding Square Root

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x^{2}.

$$x^{2}\times 1^{3}=1.5^{2}$$

Calculate 1 to the power of 3 and get 1.

$$x^{2}\times 1=1.5^{2}$$

Calculate 1.5 to the power of 2 and get 2.25.

$$x^{2}\times 1=2.25$$

Divide both sides by 1.

$$x^{2}=\frac{2.25}{1}$$

Expand \frac{2.25}{1} by multiplying both numerator and the denominator by 100.

$$x^{2}=\frac{225}{100}$$

Reduce the fraction \frac{225}{100} to lowest terms by extracting and canceling out 25.

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

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x^{2}.

$$x^{2}\times 1^{3}=1.5^{2}$$

Calculate 1 to the power of 3 and get 1.

$$x^{2}\times 1=1.5^{2}$$

Calculate 1.5 to the power of 2 and get 2.25.

$$x^{2}\times 1=2.25$$

Subtract 2.25 from both sides.

$$x^{2}\times 1-2.25=0$$

Reorder the terms.

$$x^{2}-2.25=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -2.25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-2.25\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-2.25\right)}}{2}$$

Multiply -4 times -2.25.

$$x=\frac{0±\sqrt{9}}{2}$$

Take the square root of 9.

$$x=\frac{0±3}{2}$$

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

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

Now solve the equation x=\frac{0±3}{2} when ± is minus. Divide -3 by 2.

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

The equation is now solved.

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