Solve 6x^2 15x-8 - ScanMath

Question

Simplify the expression

90 x^{3} - 8

Evaluate

6 x^{2} \times 15 x - 8

Solution

More Steps

Evaluate

6 x^{2} \times 15 x

Multiply the terms

90 x^{2} \times x

Multiply the terms with the same base by adding their exponents

90 x^{2 + 1}

Add the numbers

90 x^{3}

90 x^{3} - 8

Show Solution

Factor the expression

2 (45 x^{3} - 4)

Evaluate

6 x^{2} \times 15 x - 8

Multiply

More Steps

Evaluate

6 x^{2} \times 15 x

Multiply the terms

90 x^{2} \times x

Multiply the terms with the same base by adding their exponents

90 x^{2 + 1}

Add the numbers

90 x^{3}

90 x^{3} - 8

Solution

2 (45 x^{3} - 4)

Show Solution

Find the roots

x = \frac{3 300}{15}

Alternative Form

x \approx 0.446289

Evaluate

6 x^{2} \times 15 x - 8

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

6 x^{2} \times 15 x - 8 = 0

Multiply

More Steps

Multiply the terms

6 x^{2} \times 15 x

Multiply the terms

90 x^{2} \times x

Multiply the terms with the same base by adding their exponents

90 x^{2 + 1}

Add the numbers

90 x^{3}

90 x^{3} - 8 = 0

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

90 x^{3} = 0 + 8

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

90 x^{3} = 8

Divide both sides

\frac{90 x ^{3}}{90} = \frac{8}{90}

Divide the numbers

x^{3} = \frac{8}{90}

Cancel out the common factor 2

x^{3} = \frac{4}{45}

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

3 x^{3} = 3 \frac{4}{45}

Calculate

x = 3 \frac{4}{45}

Solution

More Steps

Evaluate

3 \frac{4}{45}

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

\frac{3 4}{3 45}

Multiply by the Conjugate

\frac{3 4 \times 3 4 5 ^{2}}{3 45 \times 3 4 5 ^{2}}

Simplify

\frac{3 4 \times 3 3 75}{3 45 \times 3 4 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

34 \times 3375

Multiply the terms

3300 \times 3

Use the commutative property to reorder the terms

33300

\frac{3 3 300}{3 45 \times 3 4 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

345 \times 3 4 5^{2}

The product of roots with the same index is equal to the root of the product

3 45 \times 4 5^{2}

Calculate the product

3 4 5^{3}

Reduce the index of the radical and exponent with 3

45

\frac{3 3 300}{45}

Cancel out the common factor 3

\frac{3 300}{15}

x = \frac{3 300}{15}

Alternative Form

x \approx 0.446289

Show Solution