Write as a Function of y square root of 1-x-6y=5

$\sqrt{1 - x} - 6 y = 5$

Add $6 y$ to both sides of the equation.

$\sqrt{1 - x} = 5 + 6 y$

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{1 - x}}^{2} = {(5 + 6 y)}^{2}$

Simplify each side of the equation.

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Multiply the exponents in ${({(1 - x)}^{\frac{1}{2}})}^{2}$ .

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Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(1 - x)}^{\frac{1}{2} \cdot 2} = {(5 + 6 y)}^{2}$

Cancel the common factor of $2$ .

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Cancel the common factor.

${(1 - x)}^{\frac{1}{2} \cdot 2} = {(5 + 6 y)}^{2}$

Rewrite the expression.

${(1 - x)}^{1} = {(5 + 6 y)}^{2}$

Simplify.

$1 - x = {(5 + 6 y)}^{2}$

Solve for $x$ .

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Simplify ${(5 + 6 y)}^{2}$ .

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Rewrite ${(5 + 6 y)}^{2}$ as $(5 + 6 y) (5 + 6 y)$ .

$1 - x = (5 + 6 y) (5 + 6 y)$

Expand $(5 + 6 y) (5 + 6 y)$ using the FOIL Method.

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Apply the distributive property.

$1 - x = 5 (5 + 6 y) + 6 y (5 + 6 y)$

Apply the distributive property.

$1 - x = 5 \cdot 5 + 5 (6 y) + 6 y (5 + 6 y)$

Apply the distributive property.

$1 - x = 5 \cdot 5 + 5 (6 y) + 6 y \cdot 5 + 6 y (6 y)$

Simplify and combine like terms.

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Simplify each term.

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Multiply $5$ by $5$ .

$1 - x = 25 + 5 (6 y) + 6 y \cdot 5 + 6 y (6 y)$

Multiply $6$ by $5$ .

$1 - x = 25 + 30 y + 6 y \cdot 5 + 6 y (6 y)$

Multiply $5$ by $6$ .

$1 - x = 25 + 30 y + 30 y + 6 y (6 y)$

Multiply $y$ by $y$ .

$1 - x = 25 + 30 y + 30 y + 6 \cdot 6 y^{2}$

Multiply $6$ by $6$ .

$1 - x = 25 + 30 y + 30 y + 36 y^{2}$

Add $30 y$ and $30 y$ .

$1 - x = 25 + 60 y + 36 y^{2}$

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

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Subtract $1$ from both sides of the equation.

$- x = 25 + 60 y + 36 y^{2} - 1$

Subtract $1$ from $25$ .

$- x = 60 y + 36 y^{2} + 24$

Multiply each term in $- x = 60 y + 36 y^{2} + 24$ by $- 1$

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Multiply each term in $- x = 60 y + 36 y^{2} + 24$ by $- 1$ .

$(- x) \cdot - 1 = 60 y \cdot - 1 + 36 y^{2} \cdot - 1 + 24 \cdot - 1$

Multiply $(- x) \cdot - 1$ .

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Multiply $- 1$ by $- 1$ .

$1 x = 60 y \cdot - 1 + 36 y^{2} \cdot - 1 + 24 \cdot - 1$

Multiply $x$ by $1$ .

$x = 60 y \cdot - 1 + 36 y^{2} \cdot - 1 + 24 \cdot - 1$

Simplify each term.

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Multiply $- 1$ by $60$ .

$x = - 60 y + 36 y^{2} \cdot - 1 + 24 \cdot - 1$

Multiply $- 1$ by $36$ .

$x = - 60 y - 36 y^{2} + 24 \cdot - 1$

Multiply $24$ by $- 1$ .

$x = - 60 y - 36 y^{2} - 24$

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

$f (y) = - 60 y - 36 y^{2} - 24$

Write as a Function of y square root of 1-x-6y=5

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