Solve (\sqrt (5x 1) 4) * (x^2 2x-15)

Question

Simplify the expression

8 x^{3} 5 x - 60 5 x

Evaluate

(5 x \times 1 \times 4) (x^{2} \times 2 x - 15)

Remove the parentheses

5 x \times 1 \times 4 (x^{2} \times 2 x - 15)

Multiply

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Multiply the terms

x^{2} \times 2 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 2

Add the numbers

x^{3} \times 2

Use the commutative property to reorder the terms

2 x^{3}

5 x \times 1 \times 4 (2 x^{3} - 15)

Multiply the terms

5 x \times 4 (2 x^{3} - 15)

Calculate the product

4 5 x \times (2 x^{3} - 15)

Multiply the terms

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Evaluate

5 x \times (2 x^{3} - 15)

Multiply each term in the parentheses by 5 x

5 x \times 2 x^{3} + 5 x \times (- 15)

Calculate the product

2 x^{3} 5 x + 5 x \times (- 15)

Calculate the product

2 x^{3} 5 x - 15 5 x

4 (2 x^{3} 5 x - 15 5 x)

Solution

More Steps

Evaluate

(2 x^{3} 5 x - 15 5 x) \times 4

Use the the distributive property to expand the expression

2 x^{3} 5 x \times 4 - 15 5 x \times 4

Multiply the terms

8 x^{3} 5 x - 15 5 x \times 4

Multiply the terms

8 x^{3} 5 x - 60 5 x

8 x^{3} 5 x - 60 5 x

Show Solution

Factor the expression

4 5 x \times (2 x^{3} - 15)

Evaluate

(5 x \times 1 \times 4) (x^{2} \times 2 x - 15)

Remove the parentheses

5 x \times 1 \times 4 (x^{2} \times 2 x - 15)

Multiply

More Steps

Multiply the terms

x^{2} \times 2 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 2

Add the numbers

x^{3} \times 2

Use the commutative property to reorder the terms

2 x^{3}

5 x \times 1 \times 4 (2 x^{3} - 15)

Multiply the terms

5 x \times 4 (2 x^{3} - 15)

Solution

More Steps

Evaluate

1 \times 4

Any expression multiplied by 1 remains the same

4

Evaluate

4 5 x

4 5 x \times (2 x^{3} - 15)

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{3 60}{2}

Alternative Form

x_{1} = 0, x_{2} \approx 1.957434

Evaluate

(5 x \times 1 \times 4) (x^{2} \times 2 x - 15)

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

(5 x \times 1 \times 4) (x^{2} \times 2 x - 15) = 0

Find the domain

More Steps

Evaluate

5 x \times 1 \geq 0

Multiply the terms

5 x \geq 0

Rewrite the expression

x \geq 0

(5 x \times 1 \times 4) (x^{2} \times 2 x - 15) = 0, x \geq 0

Calculate

(5 x \times 1 \times 4) (x^{2} \times 2 x - 15) = 0

Multiply the terms

(5 x \times 4) (x^{2} \times 2 x - 15) = 0

Calculate the product

4 5 x \times (x^{2} \times 2 x - 15) = 0

Multiply

More Steps

Multiply the terms

x^{2} \times 2 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 2

Add the numbers

x^{3} \times 2

Use the commutative property to reorder the terms

2 x^{3}

4 5 x \times (2 x^{3} - 15) = 0

Separate the equation into 2 possible cases

5 x = 0 2 x^{3} - 15 = 0

Solve the equation

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Evaluate

5 x = 0

The only way a root could be 0 is when the radicand equals 0

5 x = 0

Rewrite the expression

x = 0

x = 0 2 x^{3} - 15 = 0

Solve the equation

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Evaluate

2 x^{3} - 15 = 0

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

2 x^{3} = 0 + 15

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

2 x^{3} = 15

Divide both sides

\frac{2 x ^{3}}{2} = \frac{15}{2}

Divide the numbers

x^{3} = \frac{15}{2}

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

3 x^{3} = 3 \frac{15}{2}

Calculate

x = 3 \frac{15}{2}

Simplify the root

More Steps

Evaluate

3 \frac{15}{2}

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

\frac{3 15}{3 2}

Multiply by the Conjugate

\frac{3 15 \times 3 2 ^{2}}{3 2 \times 3 2 ^{2}}

Simplify

\frac{3 15 \times 3 4}{3 2 \times 3 2 ^{2}}

Multiply the numbers

\frac{3 60}{3 2 \times 3 2 ^{2}}

Multiply the numbers

\frac{3 60}{2}

x = \frac{3 60}{2}

x = 0 x = \frac{3 60}{2}

Check if the solution is in the defined range

x = 0 x = \frac{3 60}{2}, x \geq 0

Find the intersection of the solution and the defined range

x = 0 x = \frac{3 60}{2}

Solution

x_{1} = 0, x_{2} = \frac{3 60}{2}

Alternative Form

x_{1} = 0, x_{2} \approx 1.957434

Show Solution