Write as a Function of x 4y+ square root of x=4x+(x-1)^2

$4 y + \sqrt{x} = 4 x + {(x - 1)}^{2}$

Step 1

Simplify $4 x + {(x - 1)}^{2}$ .

Simplify each term.

Rewrite ${(x - 1)}^{2}$ as $(x - 1) (x - 1)$ .

$4 y + \sqrt{x} = 4 x + (x - 1) (x - 1)$

Expand $(x - 1) (x - 1)$ using the FOIL Method.

Apply the distributive property.

$4 y + \sqrt{x} = 4 x + x (x - 1) - 1 (x - 1)$

Apply the distributive property.

$4 y + \sqrt{x} = 4 x + x \cdot x + x \cdot - 1 - 1 (x - 1)$

Apply the distributive property.

$4 y + \sqrt{x} = 4 x + x \cdot x + x \cdot - 1 - 1 x - 1 \cdot - 1$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$4 y + \sqrt{x} = 4 x + x^{2} + x \cdot - 1 - 1 x - 1 \cdot - 1$

Move $- 1$ to the left of $x$ .

$4 y + \sqrt{x} = 4 x + x^{2} - 1 \cdot x - 1 x - 1 \cdot - 1$

Rewrite $- 1 x$ as $- x$ .

$4 y + \sqrt{x} = 4 x + x^{2} - x - 1 x - 1 \cdot - 1$

Rewrite $- 1 x$ as $- x$ .

$4 y + \sqrt{x} = 4 x + x^{2} - x - x - 1 \cdot - 1$

Multiply $- 1$ by $- 1$ .

$4 y + \sqrt{x} = 4 x + x^{2} - x - x + 1$

Subtract $x$ from $- x$ .

$4 y + \sqrt{x} = 4 x + x^{2} - 2 x + 1$

Subtract $2 x$ from $4 x$ .

$4 y + \sqrt{x} = x^{2} + 2 x + 1$

Step 2

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

$4 y = x^{2} + 2 x + 1 - \sqrt{x}$

Step 3

Divide each term in $4 y = x^{2} + 2 x + 1 - \sqrt{x}$ by $4$ and simplify.

Divide each term in $4 y = x^{2} + 2 x + 1 - \sqrt{x}$ by $4$ .

$\frac{4 y}{4} = \frac{x^{2}}{4} + \frac{2 x}{4} + \frac{1}{4} + \frac{- \sqrt{x}}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} = \frac{x^{2}}{4} + \frac{2 x}{4} + \frac{1}{4} + \frac{- \sqrt{x}}{4}$

Divide $y$ by $1$ .

$y = \frac{x^{2}}{4} + \frac{2 x}{4} + \frac{1}{4} + \frac{- \sqrt{x}}{4}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2 x$ .

$y = \frac{x^{2}}{4} + \frac{2 (x)}{4} + \frac{1}{4} + \frac{- \sqrt{x}}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$y = \frac{x^{2}}{4} + \frac{2 x}{2 \cdot 2} + \frac{1}{4} + \frac{- \sqrt{x}}{4}$

Cancel the common factor.

$y = \frac{x^{2}}{4} + \frac{2 x}{2 \cdot 2} + \frac{1}{4} + \frac{- \sqrt{x}}{4}$

Rewrite the expression.

$y = \frac{x^{2}}{4} + \frac{x}{2} + \frac{1}{4} + \frac{- \sqrt{x}}{4}$

Move the negative in front of the fraction.

$y = \frac{x^{2}}{4} + \frac{x}{2} + \frac{1}{4} - \frac{\sqrt{x}}{4}$

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.

$f (x) = \frac{x^{2}}{4} + \frac{x}{2} + \frac{1}{4} - \frac{\sqrt{x}}{4}$

Write as a Function of x 4y+ square root of x=4x+(x-1)^2

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