Solve the equation
(u-1)^2=2u^2-3u-29
for u .
(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.
To solve the equation (u-1)^2 = 2u^2 - 3u - 29 for u, we can follow these steps:
Step 1: Expand both sides of the equation.
(u-1)^2 = 2u^2 - 3u - 29 expands to:
u^2 - 2u + 1 = 2u^2 - 3u - 29
Step 2: Rearrange the terms to form a quadratic equation.
Move all terms to one side of the equation:
0 = 2u^2 - 3u - 29 - u^2 + 2u - 1
Simplifying further:
0 = u^2 - u - 30
Step 3: Factorize the quadratic equation.
To factorize the quadratic equation, we need to find two numbers that multiply to -30 and add up to -1.
In this case, the numbers are -6 and 5:
0 = (u - 6)(u + 5)
Step 4: Set each factor equal to zero and solve for u.
Setting (u - 6) equal to zero:
u - 6 = 0
u = 6
Setting (u + 5) equal to zero:
u + 5 = 0
u = -5
Therefore, the solutions to the equation (u-1)^2 = 2u^2 - 3u - 29 are u = 6 and u = -5.