Solve 9x^2 18x-7 - ScanMath

Question

Simplify the expression

162 x^{3} - 7

Evaluate

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

Solution

More Steps

Evaluate

9 x^{2} \times 18 x

Multiply the terms

162 x^{2} \times x

Multiply the terms with the same base by adding their exponents

162 x^{2 + 1}

Add the numbers

162 x^{3}

162 x^{3} - 7

Show Solution

x = \frac{3 252}{18}

Alternative Form

x \approx 0.350909

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

9 x^{2} \times 18 x

Multiply the terms

162 x^{2} \times x

Multiply the terms with the same base by adding their exponents

162 x^{2 + 1}

Add the numbers

162 x^{3}

162 x^{3} - 7 = 0

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

162 x^{3} = 0 + 7

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

162 x^{3} = 7

Divide both sides

\frac{162 x ^{3}}{162} = \frac{7}{162}

Divide the numbers

x^{3} = \frac{7}{162}

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

3 x^{3} = 3 \frac{7}{162}

Calculate

x = 3 \frac{7}{162}

Solution

More Steps

Evaluate

3 \frac{7}{162}

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

\frac{3 7}{3 162}

Simplify the radical expression

More Steps

Evaluate

3162

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

3 27 \times 6

Write the number in exponential form with the base of 3

3 3^{3} \times 6

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

3 3^{3} \times 36

Reduce the index of the radical and exponent with 3

336

\frac{3 7}{3 3 6}

Multiply by the Conjugate

\frac{3 7 \times 3 6 ^{2}}{3 3 6 \times 3 6 ^{2}}

Simplify

\frac{3 7 \times 3 36}{3 3 6 \times 3 6 ^{2}}

Multiply the numbers

More Steps

Evaluate

37 \times 336

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

3 7 \times 36

Calculate the product

3252

\frac{3 252}{3 3 6 \times 3 6 ^{2}}

Multiply the numbers

More Steps

Evaluate

336 \times 3 6^{2}

Multiply the terms

3 \times 6

Multiply the terms

18

\frac{3 252}{18}

x = \frac{3 252}{18}

Alternative Form

x \approx 0.350909

Show Solution