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Simplifying (-5y2 + 4y + -2) + (y2 + 7y + 3) = 0 Reorder the terms: (-2 + 4y + -5y2) + (y2 + 7y + 3) = 0 Remove parenthesis around (-2 + 4y + -5y2) -2 + 4y + -5y2 + (y2 + 7y + 3) = 0 Reorder the terms: -2 + 4y + -5y2 + (3 + 7y + y2) = 0 Remove parenthesis around (3 + 7y + y2) -2 + 4y + -5y2 + 3 + 7y + y2 = 0 Reorder the terms: -2 + 3 + 4y + 7y + -5y2 + y2 = 0 Combine like terms: -2 + 3 = 1 1 + 4y + 7y + -5y2 + y2 = 0 Combine like terms: 4y + 7y = 11y 1 + 11y + -5y2 + y2 = 0 Combine like terms: -5y2 + y2 = -4y2 1 + 11y + -4y2 = 0 Solving 1 + 11y + -4y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.25 + -2.75y + y2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -2.75y + 0.25 + y2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -2.75y + y2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -2.75y + y2 = 0 + 0.25 -2.75y + y2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -2.75y + y2 = 0.25 The y term is -2.75y. Take half its coefficient (-1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. -2.75y + 1.890625 + y2 = 0.25 + 1.890625 Reorder the terms: 1.890625 + -2.75y + y2 = 0.25 + 1.890625 Combine like terms: 0.25 + 1.890625 = 2.140625 1.890625 + -2.75y + y2 = 2.140625 Factor a perfect square on the left side: (y + -1.375)(y + -1.375) = 2.140625 Calculate the square root of the right side: 1.463087489 Break this problem into two subproblems by setting (y + -1.375) equal to 1.463087489 and -1.463087489.Subproblem 1
y + -1.375 = 1.463087489 Simplifying y + -1.375 = 1.463087489 Reorder the terms: -1.375 + y = 1.463087489 Solving -1.375 + y = 1.463087489 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + y = 1.463087489 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + y = 1.463087489 + 1.375 y = 1.463087489 + 1.375 Combine like terms: 1.463087489 + 1.375 = 2.838087489 y = 2.838087489 Simplifying y = 2.838087489Subproblem 2
y + -1.375 = -1.463087489 Simplifying y + -1.375 = -1.463087489 Reorder the terms: -1.375 + y = -1.463087489 Solving -1.375 + y = -1.463087489 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + y = -1.463087489 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + y = -1.463087489 + 1.375 y = -1.463087489 + 1.375 Combine like terms: -1.463087489 + 1.375 = -0.088087489 y = -0.088087489 Simplifying y = -0.088087489Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.838087489, -0.088087489}
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