I have to solve this equation by extracting square roots.
(x-7)^2=(x+3)^2
take the square root of both sides to get
±(x-7) = ±(x+3) which resolves into
x+7 = x+3 or x+7 = -x-3
the first gives no solution but the second part yields
x = 2
Check:
Left side = (2-7)^2
=(-5)^2
=25
Right side = (2+3)^2
= 25
so x=2 is the correct solution
Maybe I am not getting how you are getting 2 because I keep getting 5 when I try to solve for x+7=-x-3. It turns out like 2x=-10
Never mind, I got it now.
my typo error, sorry
should have said x-7 = -x-3
2x = 4 ......
To solve the given equation using the method of extracting square roots, you need to follow these steps:
Step 1: Expand both sides of the equation.
(x - 7)^2 = (x + 3)^2
(x - 7)(x - 7) = (x + 3)(x + 3)
(x^2 - 14x + 49) = (x^2 + 6x + 9)
Step 2: Simplify the equation.
x^2 - 14x + 49 = x^2 + 6x + 9
Step 3: Combine like terms.
x^2 - x^2 - 14x - 6x = 9 - 49
-20x = -40
Step 4: Divide both sides of the equation by -20.
(-20x)/-20 = -40/-20
x = 2
So, the solution to the equation is x = 2.