I tried solving these problems and get stuck . Can you please tell me what am I suppose to do next or did I do them all wrong
1. (x+5)^2 = (x+4)^2
√(x+5)^2 = √(x+4)^2
x+5 = x+4
?
2. (4x+7)^2 = 144
√(4x+7)^2 = √144
4x+7 = 12
?
3. (x-5)^2 = 30
√(x-5)^2 = √30
x-5 = ??
for #1, you also have to consider
x+5 = -(x+4)
2x = -9
x = -9/2
#2: 4x+7 = ±12
x = 5/4 or -19/4
#3: x-5 = ±√30
x = 5 ± √30
for #1, where did you get the negative for - ( x+ 4 )
Let's go through each problem step by step and see if you made any mistakes or what you should do next:
1. (x+5)^2 = (x+4)^2
To solve this equation, you want to eliminate the square by taking the square root of both sides.
√(x+5)^2 = √(x+4)^2
However, when taking the square root, it's essential to consider both the positive and negative square roots. So, we should have:
x + 5 = ±(x + 4)
Now, let's solve for x in each case:
For x + 5 = x + 4:
x + 5 - x = x + 4 - x
5 = 4
This equation has no solution because 5 is not equal to 4.
For x + 5 = -(x + 4):
x + 5 = -x - 4
By isolating x, we have:
x + x = -5 - 4
2x = -9
x = -9/2
So the solution for this equation is x = -9/2.
2. (4x+7)^2 = 144
Similar to the first problem, we want to eliminate the square by taking the square root of both sides.
√(4x+7)^2 = √144
Remember to consider the positive and negative square roots:
4x + 7 = ±√144
Now, let's solve for x in each case:
For 4x + 7 = √144:
4x + 7 = 12
By isolating x, we get:
4x = 12 - 7
4x = 5
x = 5/4
For 4x + 7 = -√144:
4x + 7 = -12
By isolating x, we have:
4x = -12 - 7
4x = -19
x = -19/4
So the solutions for this equation are x = 5/4 and x = -19/4.
3. (x-5)^2 = 30
Again, eliminate the square by taking the square root of both sides.
√(x-5)^2 = √30
Consider both the positive and negative square roots:
x - 5 = ±√30
Now, let's solve for x in each case:
For x - 5 = √30:
x - 5 = √30
By isolating x, we have:
x = 5 + √30
For x - 5 = -√30:
x - 5 = -√30
By isolating x, we have:
x = 5 - √30
So the solutions for this equation are x = 5 + √30 and x = 5 - √30.
Remember to double-check your work and make sure all the steps are correct.