Solve for x 25x^4-625y-500=0

$25 x^{4} - 625 y - 500 = 0$

Step 1

Move all terms not containing $x$ to the right side of the equation.

Add $625 y$ to both sides of the equation.

$25 x^{4} - 500 = 625 y$

Add $500$ to both sides of the equation.

$25 x^{4} = 625 y + 500$

Step 2

Divide each term in $25 x^{4} = 625 y + 500$ by $25$ and simplify.

Divide each term in $25 x^{4} = 625 y + 500$ by $25$ .

$\frac{25 x^{4}}{25} = \frac{625 y}{25} + \frac{500}{25}$

Simplify the left side.

Cancel the common factor of $25$ .

Cancel the common factor.

$\frac{25 x^{4}}{25} = \frac{625 y}{25} + \frac{500}{25}$

Divide $x^{4}$ by $1$ .

$x^{4} = \frac{625 y}{25} + \frac{500}{25}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $625$ and $25$ .

Factor $25$ out of $625 y$ .

$x^{4} = \frac{25 (25 y)}{25} + \frac{500}{25}$

Cancel the common factors.

Factor $25$ out of $25$ .

$x^{4} = \frac{25 (25 y)}{25 (1)} + \frac{500}{25}$

Cancel the common factor.

$x^{4} = \frac{25 (25 y)}{25 \cdot 1} + \frac{500}{25}$

Rewrite the expression.

$x^{4} = \frac{25 y}{1} + \frac{500}{25}$

Divide $25 y$ by $1$ .

$x^{4} = 25 y + \frac{500}{25}$

Divide $500$ by $25$ .

$x^{4} = 25 y + 20$

Step 3

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt[4]{25 y + 20}$

Step 4

Factor $5$ out of $25 y + 20$ .

Factor $5$ out of $25 y$ .

$x = \pm \sqrt[4]{5 (5 y) + 20}$

Factor $5$ out of $20$ .

$x = \pm \sqrt[4]{5 (5 y) + 5 (4)}$

Factor $5$ out of $5 (5 y) + 5 (4)$ .

$x = \pm \sqrt[4]{5 (5 y + 4)}$

Step 5

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = \sqrt[4]{5 (5 y + 4)}$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - \sqrt[4]{5 (5 y + 4)}$

The complete solution is the result of both the positive and negative portions of the solution.

$x = \sqrt[4]{5 (5 y + 4)}$

$x = - \sqrt[4]{5 (5 y + 4)}$

$x = \sqrt[4]{5 (5 y + 4)}$

$x = - \sqrt[4]{5 (5 y + 4)}$

Solve for x 25x^4-625y-500=0

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