Solve (1,5)^3=(3,9)^3/x^2

$$( 1,5 ) ^ { 3 } = \frac { ( 3,9 ) ^ { 3 } } { x ^ { 2 } }$$

Solve for x

$$x = \frac{13 \sqrt{65}}{25} \approx 4.192374029$$

$$x = -\frac{13 \sqrt{65}}{25} \approx -4.192374029$$

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}.

$$x^{2}\times 1,5^{3}=3,9^{3}$$

Calculate 1,5 to the power of 3 and get 3,375.

$$x^{2}\times 3,375=3,9^{3}$$

Calculate 3,9 to the power of 3 and get 59,319.

$$x^{2}\times 3,375=59,319$$

Divide both sides by 3,375.

$$x^{2}=\frac{59,319}{3,375}$$

Expand \frac{59,319}{3,375} by multiplying both numerator and the denominator by 1000.

$$x^{2}=\frac{59319}{3375}$$

Reduce the fraction \frac{59319}{3375} to lowest terms by extracting and canceling out 27.

$$x^{2}=\frac{2197}{125}$$

Take the square root of both sides of the equation.

$$x=\frac{13\sqrt{65}}{25} x=-\frac{13\sqrt{65}}{25}$$

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}.

$$x^{2}\times 1,5^{3}=3,9^{3}$$

Calculate 1,5 to the power of 3 and get 3,375.

$$x^{2}\times 3,375=3,9^{3}$$

Calculate 3,9 to the power of 3 and get 59,319.

$$x^{2}\times 3,375=59,319$$

Subtract 59,319 from both sides.

$$x^{2}\times 3,375-59,319=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$3,375x^{2}-59,319=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3,375 for a, 0 for b, and -59,319 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3,375\left(-59,319\right)}}{2\times 3,375}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3,375\left(-59,319\right)}}{2\times 3,375}$$

Multiply -4 times 3,375.

$$x=\frac{0±\sqrt{-13,5\left(-59,319\right)}}{2\times 3,375}$$

Multiply -13,5 times -59,319 by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$x=\frac{0±\sqrt{800,8065}}{2\times 3,375}$$

Take the square root of 800,8065.

$$x=\frac{0±\frac{351\sqrt{65}}{100}}{2\times 3,375}$$

Multiply 2 times 3,375.

$$x=\frac{0±\frac{351\sqrt{65}}{100}}{6,75}$$

Now solve the equation x=\frac{0±\frac{351\sqrt{65}}{100}}{6,75} when ± is plus.

$$x=\frac{13\sqrt{65}}{25}$$

Now solve the equation x=\frac{0±\frac{351\sqrt{65}}{100}}{6,75} when ± is minus.

$$x=-\frac{13\sqrt{65}}{25}$$

The equation is now solved.

$$x=\frac{13\sqrt{65}}{25} x=-\frac{13\sqrt{65}}{25}$$