# How do you solve #(2x-1)^2 +｜2x-1｜-12 =0#?

#{ (2x-1 = 3), (2x-1 = -3) :}#

with the solutions

By signing up, you agree to our Terms of Service and Privacy Policy

To solve the equation ( (2x-1)^2 + |2x-1| - 12 = 0 ), we can treat ( |2x-1| ) as a separate variable. Let ( y = |2x-1| ). Then we have two cases:

- When ( 2x-1 \geq 0 ), then ( |2x-1| = 2x-1 ).
- When ( 2x-1 < 0 ), then ( |2x-1| = -(2x-1) = 1-2x ).

Now we solve each case:

Case 1: ( 2x-1 \geq 0 ) ( (2x-1)^2 + (2x-1) - 12 = 0 ) ( (2x-1)(2x-1 + 1) - 12 = 0 ) ( (2x-1)(2x) - 12 = 0 ) ( 4x^2 - 2x - 24 = 0 ) ( 2x^2 - x - 12 = 0 )

Case 2: ( 2x-1 < 0 ) ( (2x-1)^2 + (1-2x) - 12 = 0 ) ( (2x-1)(2x-1) + (1-2x) - 12 = 0 ) ( (2x-1)(2x-1 - 1) + (1-2x) - 12 = 0 ) ( (2x-1)(2x-2) - 2x + 1 - 12 = 0 ) ( (2x-1)(2(x-1)) - 2x - 11 = 0 ) ( 2(x-1)(2x-1) - 2x - 11 = 0 ) ( 4x^2 - 6x + 1 - 2x - 11 = 0 ) ( 4x^2 - 8x - 10 = 0 ) ( 2x^2 - 4x - 5 = 0 )

Now solve each quadratic equation for ( x ).

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you solve and graph #abs(-2c-3)> -4#?
- How do you solve #abs(x-a)<=a#?
- How do you simplify #abs(3)#?
- How do you solve for #h#? #-4h+3+7h≥9h-21#
- The probability that Ruby receives junk mail is 11 percent. If she receives 94 pieces of mail in a week, about how many of them can she expect ti be junk mail?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7