So how would you break down the problem (2x-5) ^2=49

First, simplify the equation.

4x2-20x+25 = 49

Step 2: Subtract 49 from both sides.

4x2-20x+25 = 49 - 49

4x2-20x - 24 = 0

Step 3: Factor left side of equation.

4 (x+1) (x-6) = 0

Step 4: Set factors equal to 0.

x+1 = 0 or x - 6 = 0

Your answers:

x = - 1 or x = 6

To solve this you first expand the brackets.

4x^2 - 20x + 25 = 49

Then make it equal 0.

4x^2 - 20x - 24 = 0

Now solve the quardratic.

x^2 - 5x - 6 = 0

(x - 6) (x + 1) = 0

x = 6 or x = - 1