Simplifying
3y2 + -2.55y + -1.0 = 0.5
Reorder the terms:
-1.0 + -2.55y + 3y2 = 0.5
Solving
-1.0 + -2.55y + 3y2 = 0.5
Solving for variable 'y'.
Reorder the terms:
-1.0 + -0.5 + -2.55y + 3y2 = 0.5 + -0.5
Combine like terms: -1.0 + -0.5 = -1.5
-1.5 + -2.55y + 3y2 = 0.5 + -0.5
Combine like terms: 0.5 + -0.5 = 0.0
-1.5 + -2.55y + 3y2 = 0.0
Begin completing the square. Divide all terms by
3 the coefficient of the squared term:
Divide each side by '3'.
-0.5 + -0.85y + y2 = 0.0
Move the constant term to the right:
Add '0.5' to each side of the equation.
-0.5 + -0.85y + 0.5 + y2 = 0.0 + 0.5
Reorder the terms:
-0.5 + 0.5 + -0.85y + y2 = 0.0 + 0.5
Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -0.85y + y2 = 0.0 + 0.5
-0.85y + y2 = 0.0 + 0.5
Combine like terms: 0.0 + 0.5 = 0.5
-0.85y + y2 = 0.5
The y term is -0.85y. Take half its coefficient (-0.425).
Square it (0.180625) and add it to both sides.
Add '0.180625' to each side of the equation.
-0.85y + 0.180625 + y2 = 0.5 + 0.180625
Reorder the terms:
0.180625 + -0.85y + y2 = 0.5 + 0.180625
Combine like terms: 0.5 + 0.180625 = 0.680625
0.180625 + -0.85y + y2 = 0.680625
Factor a perfect square on the left side:
(y + -0.425)(y + -0.425) = 0.680625
Calculate the square root of the right side: 0.825
Break this problem into two subproblems by setting
(y + -0.425) equal to 0.825 and -0.825.
Subproblem 1
y + -0.425 = 0.825
Simplifying
y + -0.425 = 0.825
Reorder the terms:
-0.425 + y = 0.825
Solving
-0.425 + y = 0.825
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Add '0.425' to each side of the equation.
-0.425 + 0.425 + y = 0.825 + 0.425
Combine like terms: -0.425 + 0.425 = 0.000
0.000 + y = 0.825 + 0.425
y = 0.825 + 0.425
Combine like terms: 0.825 + 0.425 = 1.25
y = 1.25
Simplifying
y = 1.25
Subproblem 2
y + -0.425 = -0.825
Simplifying
y + -0.425 = -0.825
Reorder the terms:
-0.425 + y = -0.825
Solving
-0.425 + y = -0.825
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Add '0.425' to each side of the equation.
-0.425 + 0.425 + y = -0.825 + 0.425
Combine like terms: -0.425 + 0.425 = 0.000
0.000 + y = -0.825 + 0.425
y = -0.825 + 0.425
Combine like terms: -0.825 + 0.425 = -0.4
y = -0.4
Simplifying
y = -0.4
Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.25, -0.4}
