Solve (x 7)(5x^(2)-2)

Question

Simplify the expression

35 x^{3} - 14 x

Evaluate

(x \times 7) (5 x^{2} - 2)

Remove the parentheses

x \times 7 (5 x^{2} - 2)

Use the commutative property to reorder the terms

7 x (5 x^{2} - 2)

Apply the distributive property

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

Multiply the terms

More Steps

Evaluate

7 x \times 5 x^{2}

Multiply the numbers

35 x \times x^{2}

Multiply the terms

More Steps

Evaluate

x \times x^{2}

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{1 + 2}

Add the numbers

x^{3}

35 x^{3}

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

Solution

35 x^{3} - 14 x

Show Solution

x_{1} = - \frac{10}{5}, x_{2} = 0, x_{3} = \frac{10}{5}

Alternative Form

x_{1} \approx - 0.632456, x_{2} = 0, x_{3} \approx 0.632456

Evaluate

(x \times 7) (5 x^{2} - 2)

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

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

Use the commutative property to reorder the terms

7 x (5 x^{2} - 2) = 0

Elimination the left coefficient

x (5 x^{2} - 2) = 0

Separate the equation into 2 possible cases

x = 0 5 x^{2} - 2 = 0

Solve the equation

More Steps

Evaluate

5 x^{2} - 2 = 0

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

5 x^{2} = 0 + 2

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

5 x^{2} = 2

Divide both sides

\frac{5 x ^{2}}{5} = \frac{2}{5}

Divide the numbers

x^{2} = \frac{2}{5}

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

x = \pm \frac{2}{5}

Simplify the expression

More Steps

Evaluate

\frac{2}{5}

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

\frac{2}{5}

Multiply by the Conjugate

\frac{2 \times 5}{5 \times 5}

Multiply the numbers

\frac{10}{5 \times 5}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{10}{5}

x = \pm \frac{10}{5}

Separate the equation into 2 possible cases

x = \frac{10}{5} x = - \frac{10}{5}

x = 0 x = \frac{10}{5} x = - \frac{10}{5}

Solution

x_{1} = - \frac{10}{5}, x_{2} = 0, x_{3} = \frac{10}{5}

Alternative Form

x_{1} \approx - 0.632456, x_{2} = 0, x_{3} \approx 0.632456

Show Solution