Simplifying
8y2 + 10y + -3 = 0
Reorder the terms:
-3 + 10y + 8y2 = 0
Solving
-3 + 10y + 8y2 = 0
Solving for variable 'y'.
Begin completing the square. Divide all terms by
8 the coefficient of the squared term:
Divide each side by '8'.
-0.375 + 1.25y + y2 = 0
Move the constant term to the right:
Add '0.375' to each side of the equation.
-0.375 + 1.25y + 0.375 + y2 = 0 + 0.375
Reorder the terms:
-0.375 + 0.375 + 1.25y + y2 = 0 + 0.375
Combine like terms: -0.375 + 0.375 = 0.000
0.000 + 1.25y + y2 = 0 + 0.375
1.25y + y2 = 0 + 0.375
Combine like terms: 0 + 0.375 = 0.375
1.25y + y2 = 0.375
The y term is 1.25y. Take half its coefficient (0.625).
Square it (0.390625) and add it to both sides.
Add '0.390625' to each side of the equation.
1.25y + 0.390625 + y2 = 0.375 + 0.390625
Reorder the terms:
0.390625 + 1.25y + y2 = 0.375 + 0.390625
Combine like terms: 0.375 + 0.390625 = 0.765625
0.390625 + 1.25y + y2 = 0.765625
Factor a perfect square on the left side:
(y + 0.625)(y + 0.625) = 0.765625
Calculate the square root of the right side: 0.875
Break this problem into two subproblems by setting
(y + 0.625) equal to 0.875 and -0.875.
Subproblem 1
y + 0.625 = 0.875
Simplifying
y + 0.625 = 0.875
Reorder the terms:
0.625 + y = 0.875
Solving
0.625 + y = 0.875
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Add '-0.625' to each side of the equation.
0.625 + -0.625 + y = 0.875 + -0.625
Combine like terms: 0.625 + -0.625 = 0.000
0.000 + y = 0.875 + -0.625
y = 0.875 + -0.625
Combine like terms: 0.875 + -0.625 = 0.25
y = 0.25
Simplifying
y = 0.25
Subproblem 2
y + 0.625 = -0.875
Simplifying
y + 0.625 = -0.875
Reorder the terms:
0.625 + y = -0.875
Solving
0.625 + y = -0.875
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Add '-0.625' to each side of the equation.
0.625 + -0.625 + y = -0.875 + -0.625
Combine like terms: 0.625 + -0.625 = 0.000
0.000 + y = -0.875 + -0.625
y = -0.875 + -0.625
Combine like terms: -0.875 + -0.625 = -1.5
y = -1.5
Simplifying
y = -1.5
Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.25, -1.5}
