%5E2-28%3D8.jpeg "(x-4)^2-28=8")
Solving the Equation (x-4)^2 - 28 = 8
This article will guide you through the steps of solving the equation (x-4)^2 - 28 = 8. We will use algebraic manipulation to isolate the variable 'x' and find its possible values.
Step 1: Isolate the squared term
To begin, we need to get the term (x-4)^2 by itself on one side of the equation. We can achieve this by adding 28 to both sides:
(x-4)^2 - 28 + 28 = 8 + 28
This simplifies to:
(x-4)^2 = 36
Step 2: Take the square root
Now we have the squared term isolated. To get rid of the square, we take the square root of both sides:
√(x-4)^2 = ±√36
Remember that taking the square root can result in both positive and negative values. This gives us:
x - 4 = ±6
Step 3: Solve for x
Finally, we need to isolate 'x'. We can do this by adding 4 to both sides:
x - 4 + 4 = ±6 + 4
This simplifies to:
x = 10 or x = -2
Conclusion
Therefore, the solutions to the equation (x-4)^2 - 28 = 8 are x = 10 and x = -2. We can verify these solutions by substituting them back into the original equation.