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Simplifying 2y2 + 7y + -12 = 0 Reorder the terms: -12 + 7y + 2y2 = 0 Solving -12 + 7y + 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'. -6 + 3.5y + y2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 3.5y + 6 + y2 = 0 + 6 Reorder the terms: -6 + 6 + 3.5y + y2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 3.5y + y2 = 0 + 6 3.5y + y2 = 0 + 6 Combine like terms: 0 + 6 = 6 3.5y + y2 = 6 The y term is 3.5y. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5y + 3.0625 + y2 = 6 + 3.0625 Reorder the terms: 3.0625 + 3.5y + y2 = 6 + 3.0625 Combine like terms: 6 + 3.0625 = 9.0625 3.0625 + 3.5y + y2 = 9.0625 Factor a perfect square on the left side: (y + 1.75)(y + 1.75) = 9.0625 Calculate the square root of the right side: 3.010398645 Break this problem into two subproblems by setting (y + 1.75) equal to 3.010398645 and -3.010398645.Subproblem 1
y + 1.75 = 3.010398645 Simplifying y + 1.75 = 3.010398645 Reorder the terms: 1.75 + y = 3.010398645 Solving 1.75 + y = 3.010398645 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + y = 3.010398645 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + y = 3.010398645 + -1.75 y = 3.010398645 + -1.75 Combine like terms: 3.010398645 + -1.75 = 1.260398645 y = 1.260398645 Simplifying y = 1.260398645Subproblem 2
y + 1.75 = -3.010398645 Simplifying y + 1.75 = -3.010398645 Reorder the terms: 1.75 + y = -3.010398645 Solving 1.75 + y = -3.010398645 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + y = -3.010398645 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + y = -3.010398645 + -1.75 y = -3.010398645 + -1.75 Combine like terms: -3.010398645 + -1.75 = -4.760398645 y = -4.760398645 Simplifying y = -4.760398645Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.260398645, -4.760398645}
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