Answer:
x=5, x=-1
Explanation:
Since both equations are equal to y, we can set them equal to each other
y = -x + 7 and y = 0.5(x - 3)2
-x + 7 = 0.5(x - 3)^2
Distribute the right hand side by Foiling
-x+7 =.5 ( x^2 -3x-3x+9)
Combine like terms
-x+7 = .5( x^2 -6x+9)
Distribute the .5
-x+7 = .5x^2 -3x+4.5
Add x to each side
-x+x+7 = .5x^2 -3x+x+4.5
7 = .5x^2 -2x+4.5
Subtract 7 from each side
7 -7= .5x^2 -2x+4.5-7
0 = .5x^2 -2x-2.5
Multiply by 2 to clear the decimals
0 = x^2 -4x -5
Factor
0 = (x-5) (x+1)
Using the zero product property
x-5=0 x+1 =0
x=5, x=-1