Algebra Examples

$3 x - y^{2} = 4 x + 25$

Step 1

Solve for $y$ .

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Step 1.1

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

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Step 1.1.1

Subtract $3 x$ from both sides of the equation.

$- y^{2} = 4 x + 25 - 3 x$

Step 1.1.2

Subtract $3 x$ from $4 x$ .

$- y^{2} = x + 25$

Step 1.2

Divide each term in $- y^{2} = x + 25$ by $- 1$ and simplify.

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Step 1.2.1

Divide each term in $- y^{2} = x + 25$ by $- 1$ .

$\frac{- y^{2}}{- 1} = \frac{x}{- 1} + \frac{25}{- 1}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Dividing two negative values results in a positive value.

$\frac{y^{2}}{1} = \frac{x}{- 1} + \frac{25}{- 1}$

Step 1.2.2.2

Divide $y^{2}$ by $1$ .

$y^{2} = \frac{x}{- 1} + \frac{25}{- 1}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Move the negative one from the denominator of $\frac{x}{- 1}$ .

$y^{2} = - 1 \cdot x + \frac{25}{- 1}$

Step 1.2.3.1.2

Rewrite $- 1 \cdot x$ as $- x$ .

$y^{2} = - x + \frac{25}{- 1}$

Step 1.2.3.1.3

Divide $25$ by $- 1$ .

$y^{2} = - x - 25$

Step 1.3

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

$y = \pm \sqrt{- x - 25}$

Step 1.4

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

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Step 1.4.1

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

$y = \sqrt{- x - 25}$

Step 1.4.2

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

$y = - \sqrt{- x - 25}$

Step 1.4.3

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

$y = \sqrt{- x - 25}$

$y = - \sqrt{- x - 25}$

$y = \sqrt{- x - 25}$

$y = - \sqrt{- x - 25}$

$y = \sqrt{- x - 25}$

$y = - \sqrt{- x - 25}$

Step 2

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$y = a x^{2} + b x + c$

Step 3

The standard form is $\sqrt{- x - 25}, - \sqrt{- x - 25}$ .

$y = \sqrt{- x - 25}$

$y = - \sqrt{- x - 25}$

Step 4