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Simplifying (y2 + -3y + -5) + -1(-1y2 + -7y + 4) = 0 Reorder the terms: (-5 + -3y + y2) + -1(-1y2 + -7y + 4) = 0 Remove parenthesis around (-5 + -3y + y2) -5 + -3y + y2 + -1(-1y2 + -7y + 4) = 0 Reorder the terms: -5 + -3y + y2 + -1(4 + -7y + -1y2) = 0 -5 + -3y + y2 + (4 * -1 + -7y * -1 + -1y2 * -1) = 0 -5 + -3y + y2 + (-4 + 7y + 1y2) = 0 Reorder the terms: -5 + -4 + -3y + 7y + y2 + 1y2 = 0 Combine like terms: -5 + -4 = -9 -9 + -3y + 7y + y2 + 1y2 = 0 Combine like terms: -3y + 7y = 4y -9 + 4y + y2 + 1y2 = 0 Combine like terms: y2 + 1y2 = 2y2 -9 + 4y + 2y2 = 0 Solving -9 + 4y + 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'. -4.5 + 2y + y2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + 2y + 4.5 + y2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + 2y + y2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + 2y + y2 = 0 + 4.5 2y + y2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 2y + y2 = 4.5 The y term is 2y. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2y + 1 + y2 = 4.5 + 1 Reorder the terms: 1 + 2y + y2 = 4.5 + 1 Combine like terms: 4.5 + 1 = 5.5 1 + 2y + y2 = 5.5 Factor a perfect square on the left side: (y + 1)(y + 1) = 5.5 Calculate the square root of the right side: 2.34520788 Break this problem into two subproblems by setting (y + 1) equal to 2.34520788 and -2.34520788.Subproblem 1
y + 1 = 2.34520788 Simplifying y + 1 = 2.34520788 Reorder the terms: 1 + y = 2.34520788 Solving 1 + y = 2.34520788 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = 2.34520788 + -1 Combine like terms: 1 + -1 = 0 0 + y = 2.34520788 + -1 y = 2.34520788 + -1 Combine like terms: 2.34520788 + -1 = 1.34520788 y = 1.34520788 Simplifying y = 1.34520788Subproblem 2
y + 1 = -2.34520788 Simplifying y + 1 = -2.34520788 Reorder the terms: 1 + y = -2.34520788 Solving 1 + y = -2.34520788 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = -2.34520788 + -1 Combine like terms: 1 + -1 = 0 0 + y = -2.34520788 + -1 y = -2.34520788 + -1 Combine like terms: -2.34520788 + -1 = -3.34520788 y = -3.34520788 Simplifying y = -3.34520788Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.34520788, -3.34520788}
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