%5E2%2B3%3D12.jpeg "(x-2)^2+3=12")
Solving the Equation (x-2)^2 + 3 = 12
This article will walk you through solving the equation (x-2)^2 + 3 = 12.
Step 1: Isolate the squared term
First, we need to isolate the term with the square. Subtract 3 from both sides of the equation:
(x-2)^2 + 3 - 3 = 12 - 3
This simplifies to:
(x-2)^2 = 9
Step 2: Take the square root
Now, we take the square root of both sides of the equation. Remember that when taking the square root, we get both a positive and a negative result.
√((x-2)^2) = ±√9
This simplifies to:
(x-2) = ±3
Step 3: Solve for x
We now have two separate equations to solve:
- x - 2 = 3
- x - 2 = -3
Solving the first equation, we add 2 to both sides:
x - 2 + 2 = 3 + 2
This gives us:
x = 5
Solving the second equation, we also add 2 to both sides:
x - 2 + 2 = -3 + 2
This gives us:
x = -1
Solution
Therefore, the solutions to the equation (x-2)^2 + 3 = 12 are x = 5 and x = -1.