Solve (x^412x^3-40x)/(x^2)

Question

Simplify the expression

\frac{12 x ^{6} - 40}{x}

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x = 0

Show Solution

x_{1} = - \frac{6 2430}{3}, x_{2} = \frac{6 2430}{3}

Alternative Form

x_{1} \approx - 1.222212, x_{2} \approx 1.222212

Evaluate

\frac{x ^{4} \times 12 x ^{3} - 40 x}{x ^{2}}

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

\frac{x ^{4} \times 12 x ^{3} - 40 x}{x ^{2}} = 0

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

\frac{x ^{4} \times 12 x ^{3} - 40 x}{x ^{2}} = 0, x \neq = 0

Calculate

\frac{x ^{4} \times 12 x ^{3} - 40 x}{x ^{2}} = 0

Multiply

More Steps

\frac{12 x ^{7} - 40 x}{x ^{2}} = 0

Divide the terms

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\frac{12 x ^{6} - 40}{x} = 0

Cross multiply

12 x^{6} - 40 = x \times 0

Simplify the equation

12 x^{6} - 40 = 0

Move the constant to the right side

12 x^{6} = 40

Divide both sides

\frac{12 x ^{6}}{12} = \frac{40}{12}

Divide the numbers

x^{6} = \frac{40}{12}

Cancel out the common factor 4

x^{6} = \frac{10}{3}

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

x = \pm 6 \frac{10}{3}

Simplify the expression

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x = \pm \frac{6 2430}{3}

Separate the equation into 2 possible cases

x = \frac{6 2430}{3} x = - \frac{6 2430}{3}

Check if the solution is in the defined range

x = \frac{6 2430}{3} x = - \frac{6 2430}{3}, x \neq = 0

Find the intersection of the solution and the defined range

x = \frac{6 2430}{3} x = - \frac{6 2430}{3}

Solution

x_{1} = - \frac{6 2430}{3}, x_{2} = \frac{6 2430}{3}

Alternative Form

x_{1} \approx - 1.222212, x_{2} \approx 1.222212

Show Solution