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Simplifying 10y2 + -5y = 35 Reorder the terms: -5y + 10y2 = 35 Solving -5y + 10y2 = 35 Solving for variable 'y'. Reorder the terms: -35 + -5y + 10y2 = 35 + -35 Combine like terms: 35 + -35 = 0 -35 + -5y + 10y2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-7 + -1y + 2y2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-7 + -1y + 2y2)' equal to zero and attempt to solve: Simplifying -7 + -1y + 2y2 = 0 Solving -7 + -1y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + -0.5y + y2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -0.5y + 3.5 + y2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -0.5y + y2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -0.5y + y2 = 0 + 3.5 -0.5y + y2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -0.5y + y2 = 3.5 The y term is -0.5y. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5y + 0.0625 + y2 = 3.5 + 0.0625 Reorder the terms: 0.0625 + -0.5y + y2 = 3.5 + 0.0625 Combine like terms: 3.5 + 0.0625 = 3.5625 0.0625 + -0.5y + y2 = 3.5625 Factor a perfect square on the left side: (y + -0.25)(y + -0.25) = 3.5625 Calculate the square root of the right side: 1.887458609 Break this problem into two subproblems by setting (y + -0.25) equal to 1.887458609 and -1.887458609.Subproblem 1
y + -0.25 = 1.887458609 Simplifying y + -0.25 = 1.887458609 Reorder the terms: -0.25 + y = 1.887458609 Solving -0.25 + y = 1.887458609 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + y = 1.887458609 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + y = 1.887458609 + 0.25 y = 1.887458609 + 0.25 Combine like terms: 1.887458609 + 0.25 = 2.137458609 y = 2.137458609 Simplifying y = 2.137458609Subproblem 2
y + -0.25 = -1.887458609 Simplifying y + -0.25 = -1.887458609 Reorder the terms: -0.25 + y = -1.887458609 Solving -0.25 + y = -1.887458609 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + y = -1.887458609 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + y = -1.887458609 + 0.25 y = -1.887458609 + 0.25 Combine like terms: -1.887458609 + 0.25 = -1.637458609 y = -1.637458609 Simplifying y = -1.637458609Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.137458609, -1.637458609}Solution
y = {2.137458609, -1.637458609}
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