Complete the square
2y^2-y-6=0
2(y^2-1/2 y -3)
add and subtract (1/4)^2
2(y^2-1/2 y +1/16 -3-1/16)=0
2(y-1/4)^2=6 1/8
(y-1/4)^2= 3 1/16=49/16
The subject is algebra, and it is not college level.
Start with
y^2 -y/2 = 3
To make the left a perfect square, add 1/16 to both sides.
y^2 - y/2 + 1/16 = 49/16
[y - (1/4)]^2 = 49/16
y - 1/4 = + or - 7/4
Add 1/4 to both sides for the two answers
To complete the square, we can follow these steps:
Step 1: Move the constant term to the other side of the equation.
2y^2 - y = 6
Step 2: Divide the coefficient of the x^2 term by 2 and square the result.
The coefficient of the y^2 term is 2. Dividing by 2 gives us 1, and squaring 1 gives us 1.
Step 3: Add the result from Step 2 to both sides of the equation.
2y^2 - y + 1 = 6 + 1
2y^2 - y + 1 = 7
Now, the left side of the equation is a perfect square trinomial. We can rewrite it as the square of a binomial.
Step 4: Rewrite the left side of the equation as a perfect square trinomial.
(√2y - 1/√2)^2 = 7
Step 5: Take the square root of both sides of the equation.
√((√2y - 1/√2)^2) = √7
√2y - 1/√2 = ±√7
Step 6: Solve for y.
√2y = 1/√2 ± √7
2y = (1/√2 ± √7)^2
2y = (1 ± √14)^2
2y = 1 ± 2√14 + 14
y = (1 ± 2√14 + 14)/2
y = (15 ± 2√14)/2
y = 7.5 ± √14
Therefore, the solutions to the equation 2y^2 - y - 6 = 0 are y = 7.5 + √14 and y = 7.5 - √14.