Solve 2(x^2 4x-5)-1

Question

Simplify the expression

8 x^{3} - 11

Evaluate

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

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}

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

Expand the expression

More Steps

Calculate

2 (4 x^{3} - 5)

Apply the distributive property

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

Multiply the numbers

8 x^{3} - 2 \times 5

Multiply the numbers

8 x^{3} - 10

8 x^{3} - 10 - 1

Solution

8 x^{3} - 11

Show Solution

Find the roots

x = \frac{3 11}{2}

Alternative Form

x \approx 1.11199

Evaluate

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

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

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

2 (4 x^{3} - 5) - 1 = 0

Calculate

More Steps

Evaluate

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

Expand the expression

More Steps

Calculate

2 (4 x^{3} - 5)

Apply the distributive property

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

Multiply the numbers

8 x^{3} - 2 \times 5

Multiply the numbers

8 x^{3} - 10

8 x^{3} - 10 - 1

Subtract the numbers

8 x^{3} - 11

8 x^{3} - 11 = 0

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

8 x^{3} = 0 + 11

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

8 x^{3} = 11

Divide both sides

\frac{8 x ^{3}}{8} = \frac{11}{8}

Divide the numbers

x^{3} = \frac{11}{8}

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

3 x^{3} = 3 \frac{11}{8}

Calculate

x = 3 \frac{11}{8}

Solution

More Steps

Evaluate

3 \frac{11}{8}

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

\frac{3 11}{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{3 11}{2}

x = \frac{3 11}{2}

Alternative Form

x \approx 1.11199

Show Solution