Solve 8x^(4)⋅10x-144

Question

Simplify the expression

80 x^{5} - 144

Evaluate

8 x^{4} \times 10 x - 144

Solution

More Steps

Evaluate

8 x^{4} \times 10 x

Multiply the terms

80 x^{4} \times x

Multiply the terms with the same base by adding their exponents

80 x^{4 + 1}

Add the numbers

80 x^{5}

80 x^{5} - 144

Show Solution

Factor the expression

16 (5 x^{5} - 9)

Evaluate

8 x^{4} \times 10 x - 144

Multiply

More Steps

Evaluate

8 x^{4} \times 10 x

Multiply the terms

80 x^{4} \times x

Multiply the terms with the same base by adding their exponents

80 x^{4 + 1}

Add the numbers

80 x^{5}

80 x^{5} - 144

Solution

16 (5 x^{5} - 9)

Show Solution

Find the roots

x = \frac{5 5625}{5}

Alternative Form

x \approx 1.124746

Evaluate

8 x^{4} \times 10 x - 144

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

8 x^{4} \times 10 x - 144 = 0

Multiply

More Steps

Multiply the terms

8 x^{4} \times 10 x

Multiply the terms

80 x^{4} \times x

Multiply the terms with the same base by adding their exponents

80 x^{4 + 1}

Add the numbers

80 x^{5}

80 x^{5} - 144 = 0

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

80 x^{5} = 0 + 144

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

80 x^{5} = 144

Divide both sides

\frac{80 x ^{5}}{80} = \frac{144}{80}

Divide the numbers

x^{5} = \frac{144}{80}

Cancel out the common factor 16

x^{5} = \frac{9}{5}

Take the 5 -th root on both sides of the equation

5 x^{5} = 5 \frac{9}{5}

Calculate

x = 5 \frac{9}{5}

Solution

More Steps

Evaluate

5 \frac{9}{5}

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

\frac{5 9}{5 5}

Multiply by the Conjugate

\frac{5 9 \times 5 5 ^{4}}{5 5 \times 5 5 ^{4}}

Simplify

\frac{5 9 \times 5 625}{5 5 \times 5 5 ^{4}}

Multiply the numbers

More Steps

Evaluate

59 \times 5625

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

5 9 \times 625

Calculate the product

55625

\frac{5 5625}{5 5 \times 5 5 ^{4}}

Multiply the numbers

More Steps

Evaluate

55 \times 5 5^{4}

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

5 5 \times 5^{4}

Calculate the product

5 5^{5}

Reduce the index of the radical and exponent with 5

5

\frac{5 5625}{5}

x = \frac{5 5625}{5}

Alternative Form

x \approx 1.124746

Show Solution