Answer:
x = sqrt(11 - y) - 2 or x = -sqrt(11 - y) - 2
Step-by-step explanation:
Solve for x:
y = -x^2 - 4 x + 7
y = -x^2 - 4 x + 7 is equivalent to -x^2 - 4 x + 7 = y:
-x^2 - 4 x + 7 = y
Multiply both sides by -1:
x^2 + 4 x - 7 = -y
Add 7 to both sides:
x^2 + 4 x = 7 - y
Add 4 to both sides:
x^2 + 4 x + 4 = 11 - y
Write the left hand side as a square:
(x + 2)^2 = 11 - y
Take the square root of both sides:
x + 2 = sqrt(11 - y) or x + 2 = -sqrt(11 - y)
Subtract 2 from both sides:
x = sqrt(11 - y) - 2 or x + 2 = -sqrt(11 - y)
Subtract 2 from both sides:
Answer: x = sqrt(11 - y) - 2 or x = -sqrt(11 - y) - 2
