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SOLUTION: How can I put this equation in the form of solving for Y? : x^2/4=〖1-y〗^2/25
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Question 391295
:
How can I put this equation in the form of solving for Y? :
x^2/4=〖1-y〗^2/25
Answer by
haileytucki(390)
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(x^(2))/(4)=((1-y)^(2))/(25)
Since y is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
((1-y)^(2))/(25)=(x^(2))/(4)
Reorder the polynomial 1-y alphabetically from left to right, starting with the highest order term.
((-y+1)^(2))/(25)=(x^(2))/(4)
Multiply each term in the equation by 25.
((-y+1)^(2))/(25)*25=(x^(2))/(4)*25
Simplify the left-hand side of the equation by canceling the common factors.
(-y+1)^(2)=(x^(2))/(4)*25
Multiply (x^(2))/(4) by 25 to get (25x^(2))/(4).
(-y+1)^(2)=(25x^(2))/(4)
Take the square root of each side of the equation to setup the solution for y.
~((-y+1)^(2))=\~((25x^(2))/(4))
Remove the perfect root factor (-y+1) under the radical to solve for y.
(-y+1)=\~((25x^(2))/(4))
Pull all perfect square roots out from under the radical. In this case, remove the 5x because it is a perfect square.
(-y+1)=\(5x)/(2)
First, substitute in the + portion of the \ to find the first solution.
(-y+1)=(5x)/(2)
Remove the parentheses around the expression -y+1.
-y+1=(5x)/(2)
Since 1 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 1 from both sides.
-y=-1+(5x)/(2)
Move all terms not containing y to the right-hand side of the equation.
-y=(5x)/(2)-1
Multiply each term in the equation by -1.
-y*-1=(5x)/(2)*-1-1*-1
Multiply -y by -1 to get y.
y=(5x)/(2)*-1-1*-1
Simplify the right-hand side of the equation by simplifying each term.
y=-(5x)/(2)+1
Next, substitute in the - portion of the \ to find the second solution.
(-y+1)=-(5x)/(2)
Remove the parentheses around the expression -y+1.
-y+1=-(5x)/(2)
Since 1 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 1 from both sides.
-y=-1-(5x)/(2)
Move all terms not containing y to the right-hand side of the equation.
-y=-(5x)/(2)-1
Multiply each term in the equation by -1.
-y*-1=-(5x)/(2)*-1-1*-1
Multiply -y by -1 to get y.
y=-(5x)/(2)*-1-1*-1
Simplify the right-hand side of the equation by simplifying each term.
y=(5x)/(2)+1
The complete solution is the result of both the + and - portions of the solution.
y=-(5x)/(2)+1,(5x)/(2)+1