Solve: 2-y=sqrt(y+4)
I need all of the steps.
I need this ASAP because this assignment is due tomorrow.
Thanks
What do you want done?? Do you want it solved for y?
If so, first square both sides, which would leave you:
(2-y)(2-y)=y+4
FOIL
4-4y+y^2=y+4
Then subtract 4 and y which would get you
y^2-5y=0
Factor out the y.
y(y-5)=0
y=0 or y=5
To solve the equation 2 - y = sqrt(y + 4), we need to isolate the variable y. Here are the steps:
Step 1: Square both sides of the equation to eliminate the square root:
(2 - y)^2 = (sqrt(y + 4))^2
Simplifying:
4 - 4y + y^2 = y + 4
Step 2: Rearrange the terms to form a quadratic equation:
y^2 - 5y = 0
Step 3: Factor out y from both terms:
y(y - 5) = 0
Step 4: Apply the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero. Set each factor equal to zero and solve for y:
y = 0 and y - 5 = 0
Solving each equation:
For y = 0:
y = 0
For y - 5 = 0:
y = 5
So, the solutions to the equation 2 - y = sqrt(y + 4) are y = 0 and y = 5.
Please note that when solving equations involving square roots, it is important to check if the solutions satisfy the original equation.