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Simplifying 3y2 + -2y + y2 + -8y + -2 = 0 Reorder the terms: -2 + -2y + -8y + 3y2 + y2 = 0 Combine like terms: -2y + -8y = -10y -2 + -10y + 3y2 + y2 = 0 Combine like terms: 3y2 + y2 = 4y2 -2 + -10y + 4y2 = 0 Solving -2 + -10y + 4y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -5y + 2y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -5y + 2y2)' equal to zero and attempt to solve: Simplifying -1 + -5y + 2y2 = 0 Solving -1 + -5y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + -2.5y + y2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -2.5y + 0.5 + y2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -2.5y + y2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -2.5y + y2 = 0 + 0.5 -2.5y + y2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -2.5y + y2 = 0.5 The y term is -2.5y. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5y + 1.5625 + y2 = 0.5 + 1.5625 Reorder the terms: 1.5625 + -2.5y + y2 = 0.5 + 1.5625 Combine like terms: 0.5 + 1.5625 = 2.0625 1.5625 + -2.5y + y2 = 2.0625 Factor a perfect square on the left side: (y + -1.25)(y + -1.25) = 2.0625 Calculate the square root of the right side: 1.436140662 Break this problem into two subproblems by setting (y + -1.25) equal to 1.436140662 and -1.436140662.Subproblem 1
y + -1.25 = 1.436140662 Simplifying y + -1.25 = 1.436140662 Reorder the terms: -1.25 + y = 1.436140662 Solving -1.25 + y = 1.436140662 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + y = 1.436140662 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + y = 1.436140662 + 1.25 y = 1.436140662 + 1.25 Combine like terms: 1.436140662 + 1.25 = 2.686140662 y = 2.686140662 Simplifying y = 2.686140662Subproblem 2
y + -1.25 = -1.436140662 Simplifying y + -1.25 = -1.436140662 Reorder the terms: -1.25 + y = -1.436140662 Solving -1.25 + y = -1.436140662 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + y = -1.436140662 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + y = -1.436140662 + 1.25 y = -1.436140662 + 1.25 Combine like terms: -1.436140662 + 1.25 = -0.186140662 y = -0.186140662 Simplifying y = -0.186140662Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.686140662, -0.186140662}Solution
y = {2.686140662, -0.186140662}
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