Solve x^2 4x - 32

Question

Simplify the expression

4 x^{3} - 32

Evaluate

x^{2} \times 4 x - 32

Solution

More Steps

Evaluate

x^{2} \times 4 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 4

Add the numbers

x^{3} \times 4

Use the commutative property to reorder the terms

4 x^{3}

4 x^{3} - 32

Show Solution

4 (x - 2) (x^{2} + 2 x + 4)

Evaluate

x^{2} \times 4 x - 32

Evaluate

More Steps

Evaluate

x^{2} \times 4 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 4

Add the numbers

x^{3} \times 4

Use the commutative property to reorder the terms

4 x^{3}

4 x^{3} - 32

Factor out 4 from the expression

4 (x^{3} - 8)

Solution

More Steps

Evaluate

x^{3} - 8

Rewrite the expression in exponential form

x^{3} - 2^{3}

Use a^{3} - b^{3} = (a - b) (a^{2} + ab + b^{2}) to factor the expression

(x - 2) (x^{2} + x \times 2 + 2^{2})

Use the commutative property to reorder the terms

(x - 2) (x^{2} + 2 x + 2^{2})

Evaluate

(x - 2) (x^{2} + 2 x + 4)

4 (x - 2) (x^{2} + 2 x + 4)

Show Solution

x = 2

Evaluate

x^{2} \times 4 x - 32

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

x^{2} \times 4 x - 32 = 0

Multiply

More Steps

Multiply the terms

x^{2} \times 4 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 4

Add the numbers

x^{3} \times 4

Use the commutative property to reorder the terms

4 x^{3}

4 x^{3} - 32 = 0

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

4 x^{3} = 0 + 32

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

4 x^{3} = 32

Divide both sides

\frac{4 x ^{3}}{4} = \frac{32}{4}

Divide the numbers

x^{3} = \frac{32}{4}

Divide the numbers

More Steps

Evaluate

\frac{32}{4}

Reduce the numbers

\frac{8}{1}

Calculate

8

x^{3} = 8

Take the 3 -th root on both sides of the equation

3 x^{3} = 38

Calculate

x = 38

Solution

More Steps

Evaluate

38

Write the number in exponential form with the base of 2

3 2^{3}

Reduce the index of the radical and exponent with 3

2

x = 2

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