Solve 3x^2x^5-x 7

Question

Simplify the expression

3 x^{7} - 7 x

Evaluate

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

Multiply

More Steps

Multiply the terms

3 x^{2} \times x^{5}

Multiply the terms with the same base by adding their exponents

3 x^{2 + 5}

Add the numbers

3 x^{7}

3 x^{7} - x \times 7

Solution

3 x^{7} - 7 x

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Factor the expression

x (3 x^{6} - 7)

Evaluate

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

Multiply

More Steps

Multiply the terms

3 x^{2} \times x^{5}

Multiply the terms with the same base by adding their exponents

3 x^{2 + 5}

Add the numbers

3 x^{7}

3 x^{7} - x \times 7

Use the commutative property to reorder the terms

3 x^{7} - 7 x

Rewrite the expression

x \times 3 x^{6} - x \times 7

Solution

x (3 x^{6} - 7)

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Find the roots

x_{1} = - \frac{6 1701}{3}, x_{2} = 0, x_{3} = \frac{6 1701}{3}

Alternative Form

x_{1} \approx - 1.151674, x_{2} = 0, x_{3} \approx 1.151674

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

3 x^{2} \times x^{5}

Multiply the terms with the same base by adding their exponents

3 x^{2 + 5}

Add the numbers

3 x^{7}

3 x^{7} - x \times 7 = 0

Use the commutative property to reorder the terms

3 x^{7} - 7 x = 0

Factor the expression

x (3 x^{6} - 7) = 0

Separate the equation into 2 possible cases

x = 0 3 x^{6} - 7 = 0

Solve the equation

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Evaluate

3 x^{6} - 7 = 0

Move the constant to the right-hand side and change its sign

3 x^{6} = 0 + 7

Removing 0 doesn't change the value,so remove it from the expression

3 x^{6} = 7

Divide both sides

\frac{3 x ^{6}}{3} = \frac{7}{3}

Divide the numbers

x^{6} = \frac{7}{3}

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

x = \pm 6 \frac{7}{3}

Simplify the expression

More Steps

Evaluate

6 \frac{7}{3}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{6 7}{6 3}

Multiply by the Conjugate

\frac{6 7 \times 6 3 ^{5}}{6 3 \times 6 3 ^{5}}

Simplify

\frac{6 7 \times 6 243}{6 3 \times 6 3 ^{5}}

Multiply the numbers

\frac{6 1701}{6 3 \times 6 3 ^{5}}

Multiply the numbers

\frac{6 1701}{3}

x = \pm \frac{6 1701}{3}

Separate the equation into 2 possible cases

x = \frac{6 1701}{3} x = - \frac{6 1701}{3}

x = 0 x = \frac{6 1701}{3} x = - \frac{6 1701}{3}

Solution

x_{1} = - \frac{6 1701}{3}, x_{2} = 0, x_{3} = \frac{6 1701}{3}

Alternative Form

x_{1} \approx - 1.151674, x_{2} = 0, x_{3} \approx 1.151674

Show Solution