Solve 9x^2 12x-1=10

Question

Solve the equation

x = \frac{3 22}{6}

Alternative Form

x \approx 0.467007

Evaluate

9 x^{2} \times 12 x - 1 = 10

Multiply

More Steps

Evaluate

9 x^{2} \times 12 x

Multiply the terms

108 x^{2} \times x

Multiply the terms with the same base by adding their exponents

108 x^{2 + 1}

Add the numbers

108 x^{3}

108 x^{3} - 1 = 10

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

108 x^{3} = 10 + 1

Add the numbers

108 x^{3} = 11

Divide both sides

\frac{108 x ^{3}}{108} = \frac{11}{108}

Divide the numbers

x^{3} = \frac{11}{108}

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

3 x^{3} = 3 \frac{11}{108}

Calculate

x = 3 \frac{11}{108}

Solution

More Steps

Evaluate

3 \frac{11}{108}

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

\frac{3 11}{3 108}

Simplify the radical expression

More Steps

Evaluate

3108

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

3 27 \times 4

Write the number in exponential form with the base of 3

3 3^{3} \times 4

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

3 3^{3} \times 34

Reduce the index of the radical and exponent with 3

334

\frac{3 11}{3 3 4}

Multiply by the Conjugate

\frac{3 11 \times 3 4 ^{2}}{3 3 4 \times 3 4 ^{2}}

Simplify

\frac{3 11 \times 2 3 2}{3 3 4 \times 3 4 ^{2}}

Multiply the numbers

More Steps

Evaluate

311 \times 232

Multiply the terms

322 \times 2

Use the commutative property to reorder the terms

2322

\frac{2 3 22}{3 3 4 \times 3 4 ^{2}}

Multiply the numbers

More Steps

Evaluate

334 \times 3 4^{2}

Multiply the terms

3 \times 2^{2}

Multiply the terms

12

\frac{2 3 22}{12}

Cancel out the common factor 2

\frac{3 22}{6}

x = \frac{3 22}{6}

Alternative Form

x \approx 0.467007

Show Solution