Solve 6x^3 7x^2 - 5x

Question

Simplify the expression

42 x^{5} - 5 x

Evaluate

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

Solution

More Steps

Evaluate

6 x^{3} \times 7 x^{2}

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

42 x^{3 + 2}

Add the numbers

42 x^{5}

42 x^{5} - 5 x

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Factor the expression

x (42 x^{4} - 5)

Evaluate

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

Multiply

More Steps

Evaluate

6 x^{3} \times 7 x^{2}

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

42 x^{3 + 2}

Add the numbers

42 x^{5}

42 x^{5} - 5 x

Rewrite the expression

x \times 42 x^{4} - x \times 5

Solution

x (42 x^{4} - 5)

Show Solution

Find the roots

x_{1} = - \frac{4 5 \times 4 2 ^{3}}{42}, x_{2} = 0, x_{3} = \frac{4 5 \times 4 2 ^{3}}{42}

Alternative Form

x_{1} \approx - 0.587395, x_{2} = 0, x_{3} \approx 0.587395

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

6 x^{3} \times 7 x^{2}

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

42 x^{3 + 2}

Add the numbers

42 x^{5}

42 x^{5} - 5 x = 0

Factor the expression

x (42 x^{4} - 5) = 0

Separate the equation into 2 possible cases

x = 0 42 x^{4} - 5 = 0

Solve the equation

More Steps

Evaluate

42 x^{4} - 5 = 0

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

42 x^{4} = 0 + 5

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

42 x^{4} = 5

Divide both sides

\frac{42 x ^{4}}{42} = \frac{5}{42}

Divide the numbers

x^{4} = \frac{5}{42}

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

x = \pm 4 \frac{5}{42}

Simplify the expression

More Steps

Evaluate

4 \frac{5}{42}

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

\frac{4 5}{4 42}

Multiply by the Conjugate

\frac{4 5 \times 4 4 2 ^{3}}{4 42 \times 4 4 2 ^{3}}

The product of roots with the same index is equal to the root of the product

\frac{4 5 \times 4 2 ^{3}}{4 42 \times 4 4 2 ^{3}}

Multiply the numbers

\frac{4 5 \times 4 2 ^{3}}{42}

x = \pm \frac{4 5 \times 4 2 ^{3}}{42}

Separate the equation into 2 possible cases

x = \frac{4 5 \times 4 2 ^{3}}{42} x = - \frac{4 5 \times 4 2 ^{3}}{42}

x = 0 x = \frac{4 5 \times 4 2 ^{3}}{42} x = - \frac{4 5 \times 4 2 ^{3}}{42}

Solution

x_{1} = - \frac{4 5 \times 4 2 ^{3}}{42}, x_{2} = 0, x_{3} = \frac{4 5 \times 4 2 ^{3}}{42}

Alternative Form

x_{1} \approx - 0.587395, x_{2} = 0, x_{3} \approx 0.587395

Show Solution