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Simplifying 2y2 + 10y = y2 + 4y + -3 Reorder the terms: 10y + 2y2 = y2 + 4y + -3 Reorder the terms: 10y + 2y2 = -3 + 4y + y2 Solving 10y + 2y2 = -3 + 4y + y2 Solving for variable 'y'. Reorder the terms: 3 + 10y + -4y + 2y2 + -1y2 = -3 + 4y + y2 + 3 + -4y + -1y2 Combine like terms: 10y + -4y = 6y 3 + 6y + 2y2 + -1y2 = -3 + 4y + y2 + 3 + -4y + -1y2 Combine like terms: 2y2 + -1y2 = 1y2 3 + 6y + 1y2 = -3 + 4y + y2 + 3 + -4y + -1y2 Reorder the terms: 3 + 6y + 1y2 = -3 + 3 + 4y + -4y + y2 + -1y2 Combine like terms: -3 + 3 = 0 3 + 6y + 1y2 = 0 + 4y + -4y + y2 + -1y2 3 + 6y + 1y2 = 4y + -4y + y2 + -1y2 Combine like terms: 4y + -4y = 0 3 + 6y + 1y2 = 0 + y2 + -1y2 3 + 6y + 1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 3 + 6y + 1y2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 6y + -3 + y2 = 0 + -3 Reorder the terms: 3 + -3 + 6y + y2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 6y + y2 = 0 + -3 6y + y2 = 0 + -3 Combine like terms: 0 + -3 = -3 6y + y2 = -3 The y term is 6y. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6y + 9 + y2 = -3 + 9 Reorder the terms: 9 + 6y + y2 = -3 + 9 Combine like terms: -3 + 9 = 6 9 + 6y + y2 = 6 Factor a perfect square on the left side: (y + 3)(y + 3) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (y + 3) equal to 2.449489743 and -2.449489743.Subproblem 1
y + 3 = 2.449489743 Simplifying y + 3 = 2.449489743 Reorder the terms: 3 + y = 2.449489743 Solving 3 + y = 2.449489743 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y = 2.449489743 + -3 Combine like terms: 3 + -3 = 0 0 + y = 2.449489743 + -3 y = 2.449489743 + -3 Combine like terms: 2.449489743 + -3 = -0.550510257 y = -0.550510257 Simplifying y = -0.550510257Subproblem 2
y + 3 = -2.449489743 Simplifying y + 3 = -2.449489743 Reorder the terms: 3 + y = -2.449489743 Solving 3 + y = -2.449489743 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y = -2.449489743 + -3 Combine like terms: 3 + -3 = 0 0 + y = -2.449489743 + -3 y = -2.449489743 + -3 Combine like terms: -2.449489743 + -3 = -5.449489743 y = -5.449489743 Simplifying y = -5.449489743Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.550510257, -5.449489743}
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