Solve x 9x^2-6b^2x-(a^4-b^4)=0

Question

Solve the equation

Solve for a

Solve for b

a = 4 9 x^{3} - 6 b^{2} x + b^{4} a = - 4 9 x^{3} - 6 b^{2} x + b^{4}

Evaluate

x \times 9 x^{2} - 6 b^{2} x - (a^{4} - b^{4}) = 0

Simplify

More Steps

Evaluate

x \times 9 x^{2} - 6 b^{2} x - (a^{4} - b^{4})

Multiply

More Steps

Multiply the terms

x \times 9 x^{2}

Multiply the terms with the same base by adding their exponents

x^{1 + 2} \times 9

Add the numbers

x^{3} \times 9

Use the commutative property to reorder the terms

9 x^{3}

9 x^{3} - 6 b^{2} x - (a^{4} - b^{4})

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

9 x^{3} - 6 b^{2} x - a^{4} + b^{4}

9 x^{3} - 6 b^{2} x - a^{4} + b^{4} = 0

Rewrite the expression

9 x^{3} - 6 b^{2} x + b^{4} - a^{4} = 0

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

- a^{4} = 0 - (9 x^{3} - 6 b^{2} x + b^{4})

Subtract the terms

More Steps

Evaluate

0 - (9 x^{3} - 6 b^{2} x + b^{4})

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 - 9 x^{3} + 6 b^{2} x - b^{4}

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

- 9 x^{3} + 6 b^{2} x - b^{4}

- a^{4} = - 9 x^{3} + 6 b^{2} x - b^{4}

Change the signs on both sides of the equation

a^{4} = 9 x^{3} - 6 b^{2} x + b^{4}

Take the root of both sides of the equation and remember to use both positive and negative roots

a = \pm 4 9 x^{3} - 6 b^{2} x + b^{4}

Solution

a = 4 9 x^{3} - 6 b^{2} x + b^{4} a = - 4 9 x^{3} - 6 b^{2} x + b^{4}

Show Solution