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Simplifying 10y2 + -65y + -132 = 0 Reorder the terms: -132 + -65y + 10y2 = 0 Solving -132 + -65y + 10y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -13.2 + -6.5y + y2 = 0 Move the constant term to the right: Add '13.2' to each side of the equation. -13.2 + -6.5y + 13.2 + y2 = 0 + 13.2 Reorder the terms: -13.2 + 13.2 + -6.5y + y2 = 0 + 13.2 Combine like terms: -13.2 + 13.2 = 0.0 0.0 + -6.5y + y2 = 0 + 13.2 -6.5y + y2 = 0 + 13.2 Combine like terms: 0 + 13.2 = 13.2 -6.5y + y2 = 13.2 The y term is -6.5y. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5y + 10.5625 + y2 = 13.2 + 10.5625 Reorder the terms: 10.5625 + -6.5y + y2 = 13.2 + 10.5625 Combine like terms: 13.2 + 10.5625 = 23.7625 10.5625 + -6.5y + y2 = 23.7625 Factor a perfect square on the left side: (y + -3.25)(y + -3.25) = 23.7625 Calculate the square root of the right side: 4.874679477 Break this problem into two subproblems by setting (y + -3.25) equal to 4.874679477 and -4.874679477.Subproblem 1
y + -3.25 = 4.874679477 Simplifying y + -3.25 = 4.874679477 Reorder the terms: -3.25 + y = 4.874679477 Solving -3.25 + y = 4.874679477 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + y = 4.874679477 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + y = 4.874679477 + 3.25 y = 4.874679477 + 3.25 Combine like terms: 4.874679477 + 3.25 = 8.124679477 y = 8.124679477 Simplifying y = 8.124679477Subproblem 2
y + -3.25 = -4.874679477 Simplifying y + -3.25 = -4.874679477 Reorder the terms: -3.25 + y = -4.874679477 Solving -3.25 + y = -4.874679477 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + y = -4.874679477 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + y = -4.874679477 + 3.25 y = -4.874679477 + 3.25 Combine like terms: -4.874679477 + 3.25 = -1.624679477 y = -1.624679477 Simplifying y = -1.624679477Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.124679477, -1.624679477}
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