abs x^2/2 -1 =x+3 solve algebraically
so if I divide through by 2 i get
x^2 -2= 2x+3 simplifying
x^2-2x-5 =0
solve by quadratic formula to get
=3.449 and -0.445 both of which are extraneous roots
if I take negative then I get -x^2 +2=2x+6
simplify to x^2 +2x +4 if taking using quadratic then this does not work either. What have I done wrong
x^2/2 - 1 = x+3
x^2 - 2 = 2x+6
x^2 - 2x - 8 = 0
You multiplied x by 2, but not the 3.
It seems like you made a minor mistake while simplifying the equation. Let's go through the steps again and find where the error occurred.
Starting with the equation: |x^2/2 - 1| = x + 3
Step 1: Divide through by 2:
(x^2/2 - 1)/2 = (x/2) + 3/2
Simplifying this gives: x^2/4 - 1/2 = x/2 + 3/2
Step 2: Multiply through by 4 to get rid of fractions:
x^2 - 2 = 2x + 6
Step 3: Rearrange the equation to bring all terms to one side:
x^2 - 2x - 8 = 0
Now, you can solve this quadratic equation either by factoring or by using the quadratic formula.
Quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 1, b = -2, and c = -8.
Using the quadratic formula, we have:
x = (-(-2) ± √((-2)^2 - 4(1)(-8))) / (2(1))
x = (2 ± √(4 + 32)) / 2
x = (2 ± √36) / 2
x = (2 ± 6) / 2
x = (2 + 6) / 2 or x = (2 - 6) / 2
x = 8 / 2 or x = -4 / 2
x = 4 or x = -2
Thus, the solutions to the original equation are x = 4 and x = -2.
It seems like you may have made an error at the step where you simplified (x^2/2 - 1)/2. Be sure to divide through the entire term -1/2 by 2, not just the constant term -1.