Write as a Function of x -5y+ square root of x=3x+(x-6)^2

$- 5 y + \sqrt{x} = 3 x + {(x - 6)}^{2}$

Step 1

Simplify $3 x + {(x - 6)}^{2}$ .

Simplify each term.

Rewrite ${(x - 6)}^{2}$ as $(x - 6) (x - 6)$ .

$- 5 y + \sqrt{x} = 3 x + (x - 6) (x - 6)$

Expand $(x - 6) (x - 6)$ using the FOIL Method.

Apply the distributive property.

$- 5 y + \sqrt{x} = 3 x + x (x - 6) - 6 (x - 6)$

Apply the distributive property.

$- 5 y + \sqrt{x} = 3 x + x \cdot x + x \cdot - 6 - 6 (x - 6)$

Apply the distributive property.

$- 5 y + \sqrt{x} = 3 x + x \cdot x + x \cdot - 6 - 6 x - 6 \cdot - 6$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$- 5 y + \sqrt{x} = 3 x + x^{2} + x \cdot - 6 - 6 x - 6 \cdot - 6$

Move $- 6$ to the left of $x$ .

$- 5 y + \sqrt{x} = 3 x + x^{2} - 6 \cdot x - 6 x - 6 \cdot - 6$

Multiply $- 6$ by $- 6$ .

$- 5 y + \sqrt{x} = 3 x + x^{2} - 6 x - 6 x + 36$

Subtract $6 x$ from $- 6 x$ .

$- 5 y + \sqrt{x} = 3 x + x^{2} - 12 x + 36$

Subtract $12 x$ from $3 x$ .

$- 5 y + \sqrt{x} = x^{2} - 9 x + 36$

Step 2

Subtract $\sqrt{x}$ from both sides of the equation.

$- 5 y = x^{2} - 9 x + 36 - \sqrt{x}$

Step 3

Divide each term in $- 5 y = x^{2} - 9 x + 36 - \sqrt{x}$ by $- 5$ and simplify.

Divide each term in $- 5 y = x^{2} - 9 x + 36 - \sqrt{x}$ by $- 5$ .

$\frac{- 5 y}{- 5} = \frac{x^{2}}{- 5} + \frac{- 9 x}{- 5} + \frac{36}{- 5} + \frac{- \sqrt{x}}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 y}{- 5} = \frac{x^{2}}{- 5} + \frac{- 9 x}{- 5} + \frac{36}{- 5} + \frac{- \sqrt{x}}{- 5}$

Divide $y$ by $1$ .

$y = \frac{x^{2}}{- 5} + \frac{- 9 x}{- 5} + \frac{36}{- 5} + \frac{- \sqrt{x}}{- 5}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{x^{2}}{5} + \frac{- 9 x}{- 5} + \frac{36}{- 5} + \frac{- \sqrt{x}}{- 5}$

Dividing two negative values results in a positive value.

$y = - \frac{x^{2}}{5} + \frac{(9) x}{5} + \frac{36}{- 5} + \frac{- \sqrt{x}}{- 5}$

Move the negative in front of the fraction.

$y = - \frac{x^{2}}{5} + \frac{9 x}{5} - \frac{36}{5} + \frac{- \sqrt{x}}{- 5}$

Dividing two negative values results in a positive value.

$y = - \frac{x^{2}}{5} + \frac{9 x}{5} - \frac{36}{5} + \frac{\sqrt{x}}{5}$

Step 4

To rewrite as a function of $x$ , write the equation so that $y$ is by itself on one side of the equal sign and an expression involving only $x$ is on the other side.

$f (x) = - \frac{x^{2}}{5} + \frac{9 x}{5} - \frac{36}{5} + \frac{\sqrt{x}}{5}$

Write as a Function of x -5y+ square root of x=3x+(x-6)^2

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