can you help me with this
|2x - 3|^2 - 6|2x - 3| + 5=0
I know you are goood with this stuff
Math question here.
let |2x - 3| = y then you have
y^2 - 6y + 5 = 0
(y-5)(y-1)=0
y = 5 or y = 1
or |2x - 3| = 5 or |2x - 3| = 1
So you have |2x - 3| = 5
giving you:
2x - 3 = 5 or -2x + 3 = 5
2x= 4 -2x = 2
x = 2 x = -1
repeat the same steps with |2x - 3| = 1 for 2 more answers.
To solve the equation |2x - 3|^2 - 6|2x - 3| + 5 = 0, you can follow these steps:
1. Let |2x - 3| = y. By doing this, we can replace the absolute value with a variable and simplify the equation.
2. Substitute y into the original equation. We now have y^2 - 6y + 5 = 0.
3. This quadratic equation can be factored as (y - 5)(y - 1) = 0. By setting each factor equal to zero, we get y = 5 or y = 1.
4. Now, substitute back y with |2x - 3| in each equation. We have |2x - 3| = 5 and |2x - 3| = 1.
5. Solve for x in each case. When |2x - 3| = 5, we can have two possible equations: 2x - 3 = 5 and -2x + 3 = 5.
Solving the first equation, 2x = 8 and x = 4.
Solving the second equation, -2x = 2 and x = -1.
6. Repeat the steps for the case when |2x - 3| = 1. Substituting into the equation, we have 2x - 3 = 1 and -2x + 3 = 1.
Solving the first equation, 2x = 4 and x = 2.
Solving the second equation, -2x = -2 and x = 1.
Therefore, the solution to the equation |2x - 3|^2 - 6|2x - 3| + 5 = 0 is x = 4, x = -1, x = 2, x = 1.