Solve x^(2) 12x-64=0

Question

Solve the equation

x = \frac{2 3 18}{3}

Alternative Form

x \approx 1.747161

Evaluate

x^{2} \times 12 x - 64 = 0

Multiply

More Steps

Evaluate

x^{2} \times 12 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 12

Add the numbers

x^{3} \times 12

Use the commutative property to reorder the terms

12 x^{3}

12 x^{3} - 64 = 0

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

12 x^{3} = 0 + 64

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

12 x^{3} = 64

Divide both sides

\frac{12 x ^{3}}{12} = \frac{64}{12}

Divide the numbers

x^{3} = \frac{64}{12}

Cancel out the common factor 4

x^{3} = \frac{16}{3}

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

3 x^{3} = 3 \frac{16}{3}

Calculate

x = 3 \frac{16}{3}

Solution

More Steps

Evaluate

3 \frac{16}{3}

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

\frac{3 16}{3 3}

Simplify the radical expression

More Steps

Evaluate

316

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

3 8 \times 2

Write the number in exponential form with the base of 2

3 2^{3} \times 2

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

3 2^{3} \times 32

Reduce the index of the radical and exponent with 3

232

\frac{2 3 2}{3 3}

Multiply by the Conjugate

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

Simplify

\frac{2 3 2 \times 3 9}{3 3 \times 3 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

32 \times 39

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

3 2 \times 9

Calculate the product

318

\frac{2 3 18}{3 3 \times 3 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

33 \times 3 3^{2}

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

3 3 \times 3^{2}

Calculate the product

3 3^{3}

Reduce the index of the radical and exponent with 3

3

\frac{2 3 18}{3}

x = \frac{2 3 18}{3}

Alternative Form

x \approx 1.747161

Show Solution