Solve 15x^2 42x - 9

Question

Simplify the expression

630 x^{3} - 9

Evaluate

15 x^{2} \times 42 x - 9

Solution

More Steps

Evaluate

15 x^{2} \times 42 x

Multiply the terms

630 x^{2} \times x

Multiply the terms with the same base by adding their exponents

630 x^{2 + 1}

Add the numbers

630 x^{3}

630 x^{3} - 9

Show Solution

Factor the expression

9 (70 x^{3} - 1)

Evaluate

15 x^{2} \times 42 x - 9

Multiply

More Steps

Evaluate

15 x^{2} \times 42 x

Multiply the terms

630 x^{2} \times x

Multiply the terms with the same base by adding their exponents

630 x^{2 + 1}

Add the numbers

630 x^{3}

630 x^{3} - 9

Solution

9 (70 x^{3} - 1)

Show Solution

Find the roots

x = \frac{3 4900}{70}

Alternative Form

x \approx 0.242643

Evaluate

15 x^{2} \times 42 x - 9

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

15 x^{2} \times 42 x - 9 = 0

Multiply

More Steps

Multiply the terms

15 x^{2} \times 42 x

Multiply the terms

630 x^{2} \times x

Multiply the terms with the same base by adding their exponents

630 x^{2 + 1}

Add the numbers

630 x^{3}

630 x^{3} - 9 = 0

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

630 x^{3} = 0 + 9

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

630 x^{3} = 9

Divide both sides

\frac{630 x ^{3}}{630} = \frac{9}{630}

Divide the numbers

x^{3} = \frac{9}{630}

Cancel out the common factor 9

x^{3} = \frac{1}{70}

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

3 x^{3} = 3 \frac{1}{70}

Calculate

x = 3 \frac{1}{70}

Solution

More Steps

Evaluate

3 \frac{1}{70}

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

\frac{3 1}{3 70}

Simplify the radical expression

\frac{1}{3 70}

Multiply by the Conjugate

\frac{3 7 0 ^{2}}{3 70 \times 3 7 0 ^{2}}

Simplify

\frac{3 4900}{3 70 \times 3 7 0 ^{2}}

Multiply the numbers

More Steps

Evaluate

370 \times 3 7 0^{2}

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

3 70 \times 7 0^{2}

Calculate the product

3 7 0^{3}

Reduce the index of the radical and exponent with 3

70

\frac{3 4900}{70}

x = \frac{3 4900}{70}

Alternative Form

x \approx 0.242643

Show Solution