Solve 15:(x^2)=(3^3 3):10

Question

Solve the equation

x_{1} = - \frac{5 6}{9}, x_{2} = \frac{5 6}{9}

Alternative Form

x_{1} \approx - 1.360828, x_{2} \approx 1.360828

Evaluate

15 \div x^{2} = (3^{3} \times 3) \div 10

Find the domain

More Steps

15 \div x^{2} = (3^{3} \times 3) \div 10, x \neq = 0

Rewrite the expression

\frac{15}{x ^{2}} = (3^{3} \times 3) \div 10

Simplify

More Steps

\frac{15}{x ^{2}} = \frac{3 ^{4}}{10}

Rewrite the expression

x^{2} = \frac{15 \times 10}{3 ^{4}}

Divide the terms

x^{2} = \frac{50}{3 ^{3}}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm \frac{50}{3 ^{3}}

Simplify the expression

More Steps

x = \pm \frac{5 6}{9}

Separate the equation into 2 possible cases

x = \frac{5 6}{9} x = - \frac{5 6}{9}

Check if the solution is in the defined range

x = \frac{5 6}{9} x = - \frac{5 6}{9}, x \neq = 0

Find the intersection of the solution and the defined range

x = \frac{5 6}{9} x = - \frac{5 6}{9}

Solution

x_{1} = - \frac{5 6}{9}, x_{2} = \frac{5 6}{9}

Alternative Form

x_{1} \approx - 1.360828, x_{2} \approx 1.360828

Show Solution