Solve 2x^64x-12 - ScanMath

Question

Simplify the expression

8 x^{7} - 12

Evaluate

2 x^{6} \times 4 x - 12

Solution

More Steps

Evaluate

2 x^{6} \times 4 x

Multiply the terms

8 x^{6} \times x

Multiply the terms with the same base by adding their exponents

8 x^{6 + 1}

Add the numbers

8 x^{7}

8 x^{7} - 12

Show Solution

Factor the expression

4 (2 x^{7} - 3)

Evaluate

2 x^{6} \times 4 x - 12

Multiply

More Steps

Evaluate

2 x^{6} \times 4 x

Multiply the terms

8 x^{6} \times x

Multiply the terms with the same base by adding their exponents

8 x^{6 + 1}

Add the numbers

8 x^{7}

8 x^{7} - 12

Solution

4 (2 x^{7} - 3)

Show Solution

Find the roots

x = \frac{7 192}{2}

Alternative Form

x \approx 1.059634

Evaluate

2 x^{6} \times 4 x - 12

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

2 x^{6} \times 4 x - 12 = 0

Multiply

More Steps

Multiply the terms

2 x^{6} \times 4 x

Multiply the terms

8 x^{6} \times x

Multiply the terms with the same base by adding their exponents

8 x^{6 + 1}

Add the numbers

8 x^{7}

8 x^{7} - 12 = 0

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

8 x^{7} = 0 + 12

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

8 x^{7} = 12

Divide both sides

\frac{8 x ^{7}}{8} = \frac{12}{8}

Divide the numbers

x^{7} = \frac{12}{8}

Cancel out the common factor 4

x^{7} = \frac{3}{2}

Take the 7 -th root on both sides of the equation

7 x^{7} = 7 \frac{3}{2}

Calculate

x = 7 \frac{3}{2}

Solution

More Steps

Evaluate

7 \frac{3}{2}

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

\frac{7 3}{7 2}

Multiply by the Conjugate

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

Simplify

\frac{7 3 \times 7 64}{7 2 \times 7 2 ^{6}}

Multiply the numbers

More Steps

Evaluate

73 \times 764

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

7 3 \times 64

Calculate the product

7192

\frac{7 192}{7 2 \times 7 2 ^{6}}

Multiply the numbers

More Steps

Evaluate

72 \times 7 2^{6}

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

7 2 \times 2^{6}

Calculate the product

7 2^{7}

Reduce the index of the radical and exponent with 7

2

\frac{7 192}{2}

x = \frac{7 192}{2}

Alternative Form

x \approx 1.059634

Show Solution