Solve 6x^(2) 24x-18

Question

Simplify the expression

144 x^{3} - 18

Evaluate

6 x^{2} \times 24 x - 18

Solution

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Evaluate

6 x^{2} \times 24 x

Multiply the terms

144 x^{2} \times x

Multiply the terms with the same base by adding their exponents

144 x^{2 + 1}

Add the numbers

144 x^{3}

144 x^{3} - 18

Show Solution

Factor the expression

18 (2 x - 1) (4 x^{2} + 2 x + 1)

Evaluate

6 x^{2} \times 24 x - 18

Evaluate

More Steps

Evaluate

6 x^{2} \times 24 x

Multiply the terms

144 x^{2} \times x

Multiply the terms with the same base by adding their exponents

144 x^{2 + 1}

Add the numbers

144 x^{3}

144 x^{3} - 18

Factor out 18 from the expression

18 (8 x^{3} - 1)

Solution

More Steps

Evaluate

8 x^{3} - 1

Rewrite the expression in exponential form

(2 x)^{3} - 1^{3}

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

(2 x - 1) ((2 x)^{2} + 2 x \times 1 + 1^{2})

Evaluate

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Evaluate

(2 x)^{2}

To raise a product to a power,raise each factor to that power

2^{2} x^{2}

Evaluate the power

4 x^{2}

(2 x - 1) (4 x^{2} + 2 x \times 1 + 1^{2})

Any expression multiplied by 1 remains the same

(2 x - 1) (4 x^{2} + 2 x + 1^{2})

1 raised to any power equals to 1

(2 x - 1) (4 x^{2} + 2 x + 1)

18 (2 x - 1) (4 x^{2} + 2 x + 1)

Show Solution

Find the roots

x = \frac{1}{2}

Alternative Form

x = 0.5

Evaluate

6 x^{2} \times 24 x - 18

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

6 x^{2} \times 24 x - 18 = 0

Multiply

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Multiply the terms

6 x^{2} \times 24 x

Multiply the terms

144 x^{2} \times x

Multiply the terms with the same base by adding their exponents

144 x^{2 + 1}

Add the numbers

144 x^{3}

144 x^{3} - 18 = 0

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

144 x^{3} = 0 + 18

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

144 x^{3} = 18

Divide both sides

\frac{144 x ^{3}}{144} = \frac{18}{144}

Divide the numbers

x^{3} = \frac{18}{144}

Cancel out the common factor 18

x^{3} = \frac{1}{8}

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

3 x^{3} = 3 \frac{1}{8}

Calculate

x = 3 \frac{1}{8}

Solution

More Steps

Evaluate

3 \frac{1}{8}

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

\frac{3 1}{3 8}

Simplify the radical expression

\frac{1}{3 8}

Simplify the radical expression

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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

\frac{1}{2}

x = \frac{1}{2}

Alternative Form

x = 0.5

Show Solution