Solve the equation by extracting square roots. List both the exact solutions and decimal solutions rounded to the nearest hundredth.

(x-7)squared = (x+3)squared

The equation degenerates to a straight line, so there is only one exact solution.

Expand both sides, the x² terms cancel out to leave a linear equation, then solve for x.
Hint: the left hand side is:
(x-7)²=x²-14x+49

To solve the equation by extracting square roots, we begin by taking the square root of both sides of the equation. Recall that the square root of a number "a" is denoted as √a.

Given the equation: (x - 7)^2 = (x + 3)^2

Taking the square root of both sides, we have:
√[(x - 7)^2] = √[(x + 3)^2]

Simplifying further, we get:
x - 7 = ±(x + 3)

Now, let's solve for "x" by separating the equation into two cases.

Case 1: x - 7 = (x + 3)
Solving this equation step by step:
x - 7 = x + 3
x - x = 3 + 7 (subtracting "x" from both sides)
0 = 10
Since this equation has no solution, we move on to the second case.

Case 2: x - 7 = -(x + 3)
Solving this equation step by step:
x - 7 = -x - 3
x + x = -3 + 7 (adding "x" to both sides)
2x = 4
x = 4/2
x = 2

So, the solution to the equation (x - 7)^2 = (x + 3)^2 is x = 2.

Now, let's calculate the approximate decimal solution rounded to the nearest hundredth.

Taking the original equation: (x - 7)^2 = (x + 3)^2
Plugging in x = 2:
(2 - 7)^2 = (2 + 3)^2
(-5)^2 = (5)^2
25 = 25

Therefore, the exact solution x = 2 is consistent with the equation.

In conclusion, the equation has one exact solution, x = 2, and there are no decimal solutions to consider.