Final Answer:
The values of x that satisfy the system f(x) = x^2 - 2x + 3 = -2x + 12 are x = 3 and x = -3.
Step-by-step explanation:
Step 1: Set the functions equal:
f(x) = x^2 - 2x + 3
f(x) = -2x + 12
Setting them equal:
x^2 - 2x + 3 = -2x + 12
Step 2: Combine like terms:
Move all x terms to one side:
x^2 - 2x + 2x = 12 - 3
Simplify:
x^2 = 9
Step 3: Solve the quadratic equation:
Take the square root of both sides (remembering to consider both positive and negative square roots):
√(x^2) = ±√9
x = ±3
Therefore, the values of x that make the two functions equal are x = 3 and x = -3.
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Complete Question
Consider the functions f(x) = x^2 - 2x + 3 and f(x) = -2x + 12.
Solve the quadratic equation to find the values of x that satisfy the given system.
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