Solve (x^33x^2-7x 10)/(x^5)

Question

Simplify the expression

\frac{3 x ^{4} - 70}{x ^{4}}

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x = 0

Show Solution

x_{1} = - \frac{4 1890}{3}, x_{2} = \frac{4 1890}{3}

Alternative Form

x_{1} \approx - 2.197831, x_{2} \approx 2.197831

Evaluate

\frac{x ^{3} \times 3 x ^{2} - 7 x \times 10}{x ^{5}}

To find the roots of the expression,set the expression equal to 0

\frac{x ^{3} \times 3 x ^{2} - 7 x \times 10}{x ^{5}} = 0

The only way a power can not be 0 is when the base not equals 0

\frac{x ^{3} \times 3 x ^{2} - 7 x \times 10}{x ^{5}} = 0, x \neq = 0

Calculate

\frac{x ^{3} \times 3 x ^{2} - 7 x \times 10}{x ^{5}} = 0

Multiply

More Steps

\frac{3 x ^{5} - 7 x \times 10}{x ^{5}} = 0

Multiply the terms

\frac{3 x ^{5} - 70 x}{x ^{5}} = 0

Divide the terms

More Steps

\frac{3 x ^{4} - 70}{x ^{4}} = 0

Cross multiply

3 x^{4} - 70 = x^{4} \times 0

Simplify the equation

3 x^{4} - 70 = 0

Move the constant to the right side

3 x^{4} = 70

Divide both sides

\frac{3 x ^{4}}{3} = \frac{70}{3}

Divide the numbers

x^{4} = \frac{70}{3}

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

x = \pm 4 \frac{70}{3}

Simplify the expression

More Steps

x = \pm \frac{4 1890}{3}

Separate the equation into 2 possible cases

x = \frac{4 1890}{3} x = - \frac{4 1890}{3}

Check if the solution is in the defined range

x = \frac{4 1890}{3} x = - \frac{4 1890}{3}, x \neq = 0

Find the intersection of the solution and the defined range

x = \frac{4 1890}{3} x = - \frac{4 1890}{3}

Solution

x_{1} = - \frac{4 1890}{3}, x_{2} = \frac{4 1890}{3}

Alternative Form

x_{1} \approx - 2.197831, x_{2} \approx 2.197831

Show Solution