Solve 2x^2 32x-90

Question

Simplify the expression

64 x^{3} - 90

Evaluate

2 x^{2} \times 32 x - 90

Solution

More Steps

Evaluate

2 x^{2} \times 32 x

Multiply the terms

64 x^{2} \times x

Multiply the terms with the same base by adding their exponents

64 x^{2 + 1}

Add the numbers

64 x^{3}

64 x^{3} - 90

Show Solution

Factor the expression

2 (32 x^{3} - 45)

Evaluate

2 x^{2} \times 32 x - 90

Multiply

More Steps

Evaluate

2 x^{2} \times 32 x

Multiply the terms

64 x^{2} \times x

Multiply the terms with the same base by adding their exponents

64 x^{2 + 1}

Add the numbers

64 x^{3}

64 x^{3} - 90

Solution

2 (32 x^{3} - 45)

Show Solution

Find the roots

x = \frac{3 90}{4}

Alternative Form

x \approx 1.120351

Evaluate

2 x^{2} \times 32 x - 90

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

2 x^{2} \times 32 x - 90 = 0

Multiply

More Steps

Multiply the terms

2 x^{2} \times 32 x

Multiply the terms

64 x^{2} \times x

Multiply the terms with the same base by adding their exponents

64 x^{2 + 1}

Add the numbers

64 x^{3}

64 x^{3} - 90 = 0

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

64 x^{3} = 0 + 90

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

64 x^{3} = 90

Divide both sides

\frac{64 x ^{3}}{64} = \frac{90}{64}

Divide the numbers

x^{3} = \frac{90}{64}

Cancel out the common factor 2

x^{3} = \frac{45}{32}

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

3 x^{3} = 3 \frac{45}{32}

Calculate

x = 3 \frac{45}{32}

Simplify the root

More Steps

Evaluate

3 \frac{45}{32}

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

\frac{3 45}{3 32}

Simplify the radical expression

More Steps

Evaluate

332

Write the expression as a product where the root of one of the factors can be evaluated

3 8 \times 4

Write the number in exponential form with the base of 2

3 2^{3} \times 4

The root of a product is equal to the product of the roots of each factor

3 2^{3} \times 34

Reduce the index of the radical and exponent with 3

234

\frac{3 45}{2 3 4}

Multiply by the Conjugate

\frac{3 45 \times 3 4 ^{2}}{2 3 4 \times 3 4 ^{2}}

Simplify

\frac{3 45 \times 2 3 2}{2 3 4 \times 3 4 ^{2}}

Multiply the numbers

More Steps

Evaluate

345 \times 232

Multiply the terms

390 \times 2

Use the commutative property to reorder the terms

2390

\frac{2 3 90}{2 3 4 \times 3 4 ^{2}}

Multiply the numbers

More Steps

Evaluate

234 \times 3 4^{2}

Multiply the terms

2 \times 2^{2}

Calculate the product

2^{3}

\frac{2 3 90}{2 ^{3}}

Reduce the fraction

More Steps

Evaluate

\frac{2}{2 ^{3}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{1}{2 ^{3 - 1}}

Subtract the terms

\frac{1}{2 ^{2}}

\frac{3 90}{2 ^{2}}

x = \frac{3 90}{2 ^{2}}

Solution

x = \frac{3 90}{4}

Alternative Form

x \approx 1.120351

Show Solution