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Simplifying 2y2 + 212y + 3 = 0 Reorder the terms: 3 + 212y + 2y2 = 0 Solving 3 + 212y + 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'. 1.5 + 106y + y2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + 106y + -1.5 + y2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + 106y + y2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + 106y + y2 = 0 + -1.5 106y + y2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 106y + y2 = -1.5 The y term is 106y. Take half its coefficient (53). Square it (2809) and add it to both sides. Add '2809' to each side of the equation. 106y + 2809 + y2 = -1.5 + 2809 Reorder the terms: 2809 + 106y + y2 = -1.5 + 2809 Combine like terms: -1.5 + 2809 = 2807.5 2809 + 106y + y2 = 2807.5 Factor a perfect square on the left side: (y + 53)(y + 53) = 2807.5 Calculate the square root of the right side: 52.985847167 Break this problem into two subproblems by setting (y + 53) equal to 52.985847167 and -52.985847167.Subproblem 1
y + 53 = 52.985847167 Simplifying y + 53 = 52.985847167 Reorder the terms: 53 + y = 52.985847167 Solving 53 + y = 52.985847167 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-53' to each side of the equation. 53 + -53 + y = 52.985847167 + -53 Combine like terms: 53 + -53 = 0 0 + y = 52.985847167 + -53 y = 52.985847167 + -53 Combine like terms: 52.985847167 + -53 = -0.014152833 y = -0.014152833 Simplifying y = -0.014152833Subproblem 2
y + 53 = -52.985847167 Simplifying y + 53 = -52.985847167 Reorder the terms: 53 + y = -52.985847167 Solving 53 + y = -52.985847167 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-53' to each side of the equation. 53 + -53 + y = -52.985847167 + -53 Combine like terms: 53 + -53 = 0 0 + y = -52.985847167 + -53 y = -52.985847167 + -53 Combine like terms: -52.985847167 + -53 = -105.985847167 y = -105.985847167 Simplifying y = -105.985847167Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.014152833, -105.985847167}
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