I'm a little confused at how to do this problem, could you check this to make sure I have it done right ?
(x-4)^2 = 625
(undo square by square root)
(x-2) = 25 (x+2) = 25
x = 27 x = 23
( x - 4 ) ^ 2 = 625 Take square root to both sides
+ OR - ( x - 4 ) = 25
1 solution:
x - 4 = 25 Add 4 to both sides
x - 4 + 4 = 25 + 4
x = 29
2 solution:
- ( x - 4 ) = 25
- x + 4 = 25 Subtract 4 to both sides
- x + 4 - 4 = 25 - 4
- x = 21 Multiply both sides by - 1
x = - 21
The solutions are:
x = - 21 and x = 29
Thank you, but why wouldn't the 4 be square rooted
You can square rooted only expresiion between brackets, not single number.
Ohh, thank you
In order to solve the equation successfully, you will need to follow a few steps. Let me explain the process in detail:
1. Start by rewriting the equation as follows: (x - 4)² = 625.
Note that raising a quantity to the power of 2 is the same as squaring it.
2. To undo the square, you'll want to take the square root of both sides of the equation.
The square root of (x - 4)² is simply (x - 4).
3. Taking the square root of 625 gives you two possible results: +25 and -25.
4. Set up two separate equations using these two results:
a) x - 4 = 25
b) x - 4 = -25
5. Solve for x in each equation:
a) x - 4 = 25
Adding 4 to both sides: x = 29
b) x - 4 = -25
Adding 4 to both sides: x = -21
So, the solutions to the equation (x - 4)² = 625 are x = 29 and x = -21.
Please note that you made a small mistake in your calculations: (x-2) = 25 should actually be (x-4) = 25. But apart from that, you applied the correct method to solve the equation.