SOLUTION: Find all solutions of the equation |x^2

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Question 1044821: Find all solutions of the equation |x^2 - 14x + 29| = 4.
Found 2 solutions by ikleyn, Boreal:
Answer by ikleyn(52810)   (Show Source):
You can put this solution on YOUR website!
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Find all solutions of the equation |x^2 - 14x + 29| = 4.
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This equation deploys in two independent equations:

1) = ---> = ---> = ; = , = . and 2) = ---> = ---> (x-11)*(x-3) = 0 ---> x = 11 or x = 3. Answer. = , = , = 11 and = 3.

Plots y = |x^2 - 14x + 29| and y = 4.

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Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website!
|x^2 - 14x + 29| = 4.
start with x^2-14x+29=4
x^2-14x+25=0
x=(1/2)(14+/- sqrt (196-100); sqrt 96=4 sqrt (6)
x=7+2 sqrt (6) and 7-2 sqrt (6). Numerically, these are about 11.9 and 2.1
Check and 11.9 and 2.1 are both within 0.01 (rounding error).

The other solution is when x^2-14x+29=-4, because |-4|=4.
Now x^2-14x+33=0
(x-11)(x-3)=0
x=11,3
Check in the original |121-154+29|=|-4)=4; 9-42+29=|-4|=4

Exact solutions are 7-2 sqrt(6),3,11, and 7+2 sqrt (6)

SOLUTION: Find all solutions of the equation |x^2 - 14x + 29| = 4.