Solve x^25x-(a^2 a-6)=0

Question

Solve the equation

Solve for x

Solve for a

x = \frac{3 25 a ^{3} - 150}{5}

Evaluate

x^{2} \times 5 x - (a^{2} \times a - 6) = 0

Simplify

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Evaluate

x^{2} \times 5 x - (a^{2} \times a - 6)

Multiply the terms

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Evaluate

a^{2} \times a

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

a^{2 + 1}

Add the numbers

a^{3}

x^{2} \times 5 x - (a^{3} - 6)

Multiply

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Multiply the terms

x^{2} \times 5 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 5

Add the numbers

x^{3} \times 5

Use the commutative property to reorder the terms

5 x^{3}

5 x^{3} - (a^{3} - 6)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

5 x^{3} - a^{3} + 6

5 x^{3} - a^{3} + 6 = 0

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

5 x^{3} = 0 - (- a^{3} + 6)

Subtract the terms

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Evaluate

0 - (- a^{3} + 6)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

0 + a^{3} - 6

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

a^{3} - 6

5 x^{3} = a^{3} - 6

Divide both sides

\frac{5 x ^{3}}{5} = \frac{a ^{3} - 6}{5}

Divide the numbers

x^{3} = \frac{a ^{3} - 6}{5}

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

3 x^{3} = 3 \frac{a ^{3} - 6}{5}

Calculate

x = 3 \frac{a ^{3} - 6}{5}

Solution

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Evaluate

3 \frac{a ^{3} - 6}{5}

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

\frac{3 a ^{3} - 6}{3 5}

Multiply by the Conjugate

\frac{3 a ^{3} - 6 \times 3 5 ^{2}}{3 5 \times 3 5 ^{2}}

Calculate

\frac{3 a ^{3} - 6 \times 3 5 ^{2}}{5}

Calculate

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Evaluate

3 a^{3} - 6 \times 3 5^{2}

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

3 (a^{3} - 6) \times 5^{2}

Calculate the product

3 25 a^{3} - 150

\frac{3 25 a ^{3} - 150}{5}

x = \frac{3 25 a ^{3} - 150}{5}

Show Solution