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Question 527280: solve (x+3)^2+(y-2)^=4 find the x and y intercepts
Answer by thinkinbig2(5)   (Show Source):
You can put this solution on YOUR website! (x+3)^(2)+(y-2)=4
To find the x-intercept, substitute in 0 for y and solve for x.
(x+3)^(2)+((0)-2)=4
Remove the parentheses from the numerator.
(x+3)^(2)+(0-2)=4
Combine all similar expressions.
(x+3)^(2)+(-2)=4
Move the minus sign from the numerator to the front of the expression.
(x+3)^(2)-2=4
Since -2 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 2 to both sides.
(x+3)^(2)=2+4
Add 4 to 2 to get 6.
(x+3)^(2)=6
Take the square root of each side of the equation to setup the solution for x.
~((x+3)^(2))=\~(6)
Remove the perfect root factor (x+3) under the radical to solve for x.
(x+3)=\~(6)
First, substitute in the + portion of the \ to find the first solution.
(x+3)=~(6)
Remove the parentheses around the expression x+3.
x+3=~(6)
Since 3 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 3 from both sides.
x=-3+~(6)
Move all terms not containing x to the right-hand side of the equation.
x=~(6)-3
Next, substitute in the - portion of the \ to find the second solution.
(x+3)=-~(6)
Remove the parentheses around the expression x+3.
x+3=-~(6)
Since 3 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 3 from both sides.
x=-3+-~(6)
Move all terms not containing x to the right-hand side of the equation.
x=-~(6)-3
The complete solution is the result of both the + and - portions of the solution.
x=~(6)-3,-~(6)-3
To find the y-intercept, substitute in 0 for x and solve for y.
((0)+3)^(2)+(y-2)=4
Remove the parentheses from the numerator.
(0+3)^(2)+(y-2)=4
Combine all similar expressions.
(3)^(2)+(y-2)=4
Expand the exponent (2) to the expression.
(3^(2))+(y-2)=4
Squaring a number is the same as multiplying the number by itself (3*3). In this case, 3 squared is 9.
(9)+(y-2)=4
Remove the parentheses from the numerator.
9+(y-2)=4
Remove the parentheses around the expression y-2.
9+y-2=4
Subtract 2 from 9 to get 7.
7+y=4
Since 7 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 7 from both sides.
y=-7+4
Solve the equation.
y=-3
These are the x and y intercepts of the equation (x+3)^(2)+(y-2)=4.
x=~(6)-3,-~(6)-3, y=-3
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