Solve for x over the real numbers:
sqrt(x+2) = x-4
Raise both sides to the power of two:
x+2 = (x-4)^2
Expand out terms of the right hand side:
x+2 = x^2-8 x+16
Subtract x^2-8 x+16 from both sides:
-x^2+9 x-14 = 0
The left hand side factors into a product with three terms:
-((x-7) (x-2)) = 0
Multiply both sides by -1:
(x-7) (x-2) = 0
Split into two equations:
x-7 = 0 or x-2 = 0
Add 7 to both sides:
x = 7 or x-2 = 0
Add 2 to both sides:
x = 7 or x = 2
sqrt(x+2) => sqrt(2+2) = 2
x-4 => 2-4 = -2:
So this solution is incorrect
sqrt(x+2) => sqrt(2+7) = 3
x-4 => 7-4 = 3:
So this solution is correct
The solution is:
Answer: |
| x = 7
Solve for x over the real numbers:
sqrt(x+2) = x-4
Raise both sides to the power of two:
x+2 = (x-4)^2
Expand out terms of the right hand side:
x+2 = x^2-8 x+16
Subtract x^2-8 x+16 from both sides:
-x^2+9 x-14 = 0
The left hand side factors into a product with three terms:
-((x-7) (x-2)) = 0
Multiply both sides by -1:
(x-7) (x-2) = 0
Split into two equations:
x-7 = 0 or x-2 = 0
Add 7 to both sides:
x = 7 or x-2 = 0
Add 2 to both sides:
x = 7 or x = 2
sqrt(x+2) => sqrt(2+2) = 2
x-4 => 2-4 = -2:
So this solution is incorrect
sqrt(x+2) => sqrt(2+7) = 3
x-4 => 7-4 = 3:
So this solution is correct
The solution is:
Answer: |
| x = 7
