Solve the equation
(u-1)^2=2u^2-3u-29
for u .
This was answered the first time you posted it. I pasted the answer below.
(u - 1)^2 = 2u^2 - 3u - 29
u^2 - 2u + 1 = 2u^2 - 3u - 29
u^2 - u - 30 = 0
This does not factor.
Solve by using the quadratic formula or the method of completing the square.
Post your answer and someone will check it for you.
I got 1 +or- the sqrt 90/2
u^2 - u - 30 = 0
Using the quadratic formula,
x =(-b +- (sqrt(b^2 - 4ac))/2a
a = 1, b = -1, c = -30
x = 1 +- (sqrt(-1^2 - 4(1)(-30))/2
x = (1 +- (sqrt(1 + 120))/2
x = (1 +- (sqrt(121))/2
x = (1 +- 11)/2
x = (1 + 11)/2 = 6
x = (1 - 11)/2 = -5
To solve the equation (u-1)^2 = 2u^2 - 3u - 29 for u, we can follow these steps:
Step 1: Expand the left side of the equation by multiplying (u-1) with itself.
(u-1)^2 = (u-1)(u-1)
= u(u-1) - 1(u-1)
= u^2 - u - u + 1
= u^2 - 2u + 1
Step 2: Rewrite the equation with the expanded form:
u^2 - 2u + 1 = 2u^2 - 3u - 29
Step 3: Move all terms to one side of the equation to create a quadratic equation:
0 = 2u^2 - 3u - 29 - u^2 + 2u - 1
= u^2 - u - 30
Step 4: Factorize the quadratic equation:
0 = (u - 6)(u + 5)
Step 5: Set each factor equal to zero and solve for u:
u - 6 = 0 --> u = 6
u + 5 = 0 --> u = -5
Therefore, the solutions for u are u = 6 and u = -5.