Solve for t:
√(t-108) - √(t+186) = 66
(t-108) -2[(t-108)(t+186)]^.5 +(t+186) = 4356
2 t + 78 - 4256 = 2[(t-108)(t+186)]^.5
t - 2089 = [(t-108)(t+186)]^.5
t^2 - 4178 t + 4363921 = t^2 + 78 t - 20088
4384009 = 4256 t
t = 102.9
check my arithmetic !!!
√(t-108) = √(t+186) + 66
square both sides
t-108 = t+186 + 2√(t+186) + 4356
-4650 = 2√(t+186)
by definition, √(any#) is positive, so your equation has no real solution.
As I answered your previous post of the same ?:
http://www.jiskha.com/display.cgi?id=1278659403
To solve for t in the equation √(t-108) - √(t+186) = 66, we need to isolate the variable t.
Here are the steps to solve the equation:
Step 1: Start by moving one of the square root terms to the other side of the equation. Let's move √(t+186) to the right side, so the equation becomes √(t - 108) = √(t + 186) + 66.
Step 2: Square both sides of the equation to eliminate the square root symbols. This gives us (t - 108) = (t + 186) + 2 * √(t + 186) * 66.
Step 3: Simplify the equation. Distribute the 2 to both terms inside the square root, and then square both sides again to eliminate the remaining square root. The equation becomes t - 108 = t + 186 + 132 * √(t + 186) + 4356. At this point, we have eliminated the square roots.
Step 4: Move variable terms to one side of the equation and constant terms to the other side. Subtract t from both sides to obtain -108 = 186 + 132 * √(t + 186) + 4356.
Step 5: Rearrange the equation to isolate the square root term. We get 132 * √(t + 186) = -108 - 186 - 4356.
Step 6: Simplify the equation. Combine the constant terms on the right side: -108 - 186 - 4356 = -4650. The equation now becomes 132 * √(t + 186) = -4650.
Step 7: Divide both sides of the equation by 132 to solve for √(t + 186). This gives us √(t + 186) = -4650 / 132.
Step 8: Square both sides of the equation to eliminate the square root. This results in t + 186 = (-4650 / 132)^2.
Step 9: Simplify the equation. Calculate (-4650 / 132)^2 to get a numerical value. Assume the calculated value turns out to be A, then the equation becomes t + 186 = A.
Step 10: Finally, solve for t by subtracting 186 from both sides of the equation. This gives us t = A - 186.
Hence, the value of t can be obtained by calculating A and subtracting 186 from it.