Solve 10x^55x^2-15

Question

Simplify the expression

50 x^{7} - 15

Evaluate

10 x^{5} \times 5 x^{2} - 15

Solution

More Steps

Evaluate

10 x^{5} \times 5 x^{2}

Multiply the terms

50 x^{5} \times x^{2}

Multiply the terms with the same base by adding their exponents

50 x^{5 + 2}

Add the numbers

50 x^{7}

50 x^{7} - 15

Show Solution

5 (10 x^{7} - 3)

Evaluate

10 x^{5} \times 5 x^{2} - 15

Multiply

More Steps

Evaluate

10 x^{5} \times 5 x^{2}

Multiply the terms

50 x^{5} \times x^{2}

Multiply the terms with the same base by adding their exponents

50 x^{5 + 2}

Add the numbers

50 x^{7}

50 x^{7} - 15

Solution

5 (10 x^{7} - 3)

Show Solution

x = \frac{7 3 \times 1 0 ^{6}}{10}

Alternative Form

x \approx 0.841982

Evaluate

10 x^{5} \times 5 x^{2} - 15

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

10 x^{5} \times 5 x^{2} - 15 = 0

Multiply

More Steps

Multiply the terms

10 x^{5} \times 5 x^{2}

Multiply the terms

50 x^{5} \times x^{2}

Multiply the terms with the same base by adding their exponents

50 x^{5 + 2}

Add the numbers

50 x^{7}

50 x^{7} - 15 = 0

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

50 x^{7} = 0 + 15

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

50 x^{7} = 15

Divide both sides

\frac{50 x ^{7}}{50} = \frac{15}{50}

Divide the numbers

x^{7} = \frac{15}{50}

Cancel out the common factor 5

x^{7} = \frac{3}{10}

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

7 x^{7} = 7 \frac{3}{10}

Calculate

x = 7 \frac{3}{10}

Solution

More Steps

Evaluate

7 \frac{3}{10}

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

\frac{7 3}{7 10}

Multiply by the Conjugate

\frac{7 3 \times 7 1 0 ^{6}}{7 10 \times 7 1 0 ^{6}}

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

\frac{7 3 \times 1 0 ^{6}}{7 10 \times 7 1 0 ^{6}}

Multiply the numbers

More Steps

Evaluate

710 \times 7 1 0^{6}

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

7 10 \times 1 0^{6}

Calculate the product

7 1 0^{7}

Reduce the index of the radical and exponent with 7

10

\frac{7 3 \times 1 0 ^{6}}{10}

x = \frac{7 3 \times 1 0 ^{6}}{10}

Alternative Form

x \approx 0.841982

Show Solution