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Simplifying 2y2 + -8y + 15 + -2y + 12y + -36 = 0 Reorder the terms: 15 + -36 + -8y + -2y + 12y + 2y2 = 0 Combine like terms: 15 + -36 = -21 -21 + -8y + -2y + 12y + 2y2 = 0 Combine like terms: -8y + -2y = -10y -21 + -10y + 12y + 2y2 = 0 Combine like terms: -10y + 12y = 2y -21 + 2y + 2y2 = 0 Solving -21 + 2y + 2y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -10.5 + y + y2 = 0 Move the constant term to the right: Add '10.5' to each side of the equation. -10.5 + y + 10.5 + y2 = 0 + 10.5 Reorder the terms: -10.5 + 10.5 + y + y2 = 0 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + y + y2 = 0 + 10.5 y + y2 = 0 + 10.5 Combine like terms: 0 + 10.5 = 10.5 y + y2 = 10.5 The y term is y. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + y2 = 10.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + y2 = 10.5 + 0.25 Combine like terms: 10.5 + 0.25 = 10.75 1.25 + y2 = 10.75 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = 10.75 Calculate the square root of the right side: 3.278719262 Break this problem into two subproblems by setting (y + 0.5) equal to 3.278719262 and -3.278719262.Subproblem 1
y + 0.5 = 3.278719262 Simplifying y + 0.5 = 3.278719262 Reorder the terms: 0.5 + y = 3.278719262 Solving 0.5 + y = 3.278719262 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = 3.278719262 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 3.278719262 + -0.5 y = 3.278719262 + -0.5 Combine like terms: 3.278719262 + -0.5 = 2.778719262 y = 2.778719262 Simplifying y = 2.778719262Subproblem 2
y + 0.5 = -3.278719262 Simplifying y + 0.5 = -3.278719262 Reorder the terms: 0.5 + y = -3.278719262 Solving 0.5 + y = -3.278719262 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = -3.278719262 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -3.278719262 + -0.5 y = -3.278719262 + -0.5 Combine like terms: -3.278719262 + -0.5 = -3.778719262 y = -3.778719262 Simplifying y = -3.778719262Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.778719262, -3.778719262}
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