Solve 7x^2 6x-18 - ScanMath

Question

Simplify the expression

42 x^{3} - 18

Evaluate

7 x^{2} \times 6 x - 18

Solution

More Steps

Evaluate

7 x^{2} \times 6 x

Multiply the terms

42 x^{2} \times x

Multiply the terms with the same base by adding their exponents

42 x^{2 + 1}

Add the numbers

42 x^{3}

42 x^{3} - 18

Show Solution

Factor the expression

6 (7 x^{3} - 3)

Evaluate

7 x^{2} \times 6 x - 18

Multiply

More Steps

Evaluate

7 x^{2} \times 6 x

Multiply the terms

42 x^{2} \times x

Multiply the terms with the same base by adding their exponents

42 x^{2 + 1}

Add the numbers

42 x^{3}

42 x^{3} - 18

Solution

6 (7 x^{3} - 3)

Show Solution

Find the roots

x = \frac{3 147}{7}

Alternative Form

x \approx 0.753947

Evaluate

7 x^{2} \times 6 x - 18

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

7 x^{2} \times 6 x - 18 = 0

Multiply

More Steps

Multiply the terms

7 x^{2} \times 6 x

Multiply the terms

42 x^{2} \times x

Multiply the terms with the same base by adding their exponents

42 x^{2 + 1}

Add the numbers

42 x^{3}

42 x^{3} - 18 = 0

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

42 x^{3} = 0 + 18

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

42 x^{3} = 18

Divide both sides

\frac{42 x ^{3}}{42} = \frac{18}{42}

Divide the numbers

x^{3} = \frac{18}{42}

Cancel out the common factor 6

x^{3} = \frac{3}{7}

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

3 x^{3} = 3 \frac{3}{7}

Calculate

x = 3 \frac{3}{7}

Solution

More Steps

Evaluate

3 \frac{3}{7}

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

\frac{3 3}{3 7}

Multiply by the Conjugate

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

Simplify

\frac{3 3 \times 3 49}{3 7 \times 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

33 \times 349

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

3 3 \times 49

Calculate the product

3147

\frac{3 147}{3 7 \times 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

37 \times 3 7^{2}

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

3 7 \times 7^{2}

Calculate the product

3 7^{3}

Reduce the index of the radical and exponent with 3

7

\frac{3 147}{7}

x = \frac{3 147}{7}

Alternative Form

x \approx 0.753947

Show Solution