Solve x^(2) 6x 9=7

Question

Solve the equation

x = \frac{3 28}{6}

Alternative Form

x \approx 0.506098

Evaluate

x^{2} \times 6 x \times 9 = 7

Multiply

More Steps

Evaluate

x^{2} \times 6 x \times 9

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 6 \times 9

Add the numbers

x^{3} \times 6 \times 9

Multiply the terms

x^{3} \times 54

Use the commutative property to reorder the terms

54 x^{3}

54 x^{3} = 7

Divide both sides

\frac{54 x ^{3}}{54} = \frac{7}{54}

Divide the numbers

x^{3} = \frac{7}{54}

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

3 x^{3} = 3 \frac{7}{54}

Calculate

x = 3 \frac{7}{54}

Solution

More Steps

Evaluate

3 \frac{7}{54}

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

\frac{3 7}{3 54}

Simplify the radical expression

More Steps

Evaluate

354

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

3 27 \times 2

Write the number in exponential form with the base of 3

3 3^{3} \times 2

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

3 3^{3} \times 32

Reduce the index of the radical and exponent with 3

332

\frac{3 7}{3 3 2}

Multiply by the Conjugate

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

Simplify

\frac{3 7 \times 3 4}{3 3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

37 \times 34

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

3 7 \times 4

Calculate the product

328

\frac{3 28}{3 3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

332 \times 3 2^{2}

Multiply the terms

3 \times 2

Multiply the terms

6

\frac{3 28}{6}

x = \frac{3 28}{6}

Alternative Form

x \approx 0.506098

Show Solution