Let's do this step by step:
Subtract both sides by 7
-2|x-4|= -10
Divide each side by -2
|x-4|= 5
Now since this is an absolute value equation, you will have two answers. This means you make the equation both positive and negative.
X-4= 5and -(x-4)= 5
Solve for x for both
X-4= 5: add four on both sides
X= 9
-x+ 4= 5: subtract 4 and divide by -1
X= -1
So your answer is: X= -1 , 9
The answer is -1. This is because you can plug in the negative values to see which ones work.
X^2+10x+25= 24+25
(x+5)^2= 49
x+5= +-7 (plus or minus 7)
x= -7-5
x=-12
x=7-5
x=2
Final answer: x={-12, 2}
