Question

Describe, step-by-step how to solve 5(x-3)^2-25=100

Answer 1

Here is the step-by-step solution to the equation 5(x-3)^2-25=100:

Step 1: Add 25 to both sides of the equation to isolate the expression in parentheses. This gives you 5(x-3)^2 = 125.

Step 2: Divide both sides of the equation by 5 to isolate the expression in parentheses. This gives you (x-3)^2 = 25.

Step 3: Take the square root of both sides of the equation. Remember that when you take the square root of a number, you need to consider both the positive and negative square roots. This gives you x-3 = ±5.

Step 4: Add 3 to both sides of the equation to solve for x. This gives you x = 3 ± 5.

Step 5: Simplify the expression by adding and subtracting. This gives you two possible solutions: x = 8 or x = -2.

Therefore, the solutions to the equation 5(x-3)^2-25=100 are x = 8 and x = -2.

Answer 2

Explanation:

`5.(x-3)^2 - 25 = 100\\5.(x-3)^2 = 125\\(x-3)^2 = 25\\x - 3 = 5 = > x = 8\\ or \\x - 3 = -5 = > x = -2`