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Simplifying y2 + -2y + -15 = 3 Reorder the terms: -15 + -2y + y2 = 3 Solving -15 + -2y + y2 = 3 Solving for variable 'y'. Reorder the terms: -15 + -3 + -2y + y2 = 3 + -3 Combine like terms: -15 + -3 = -18 -18 + -2y + y2 = 3 + -3 Combine like terms: 3 + -3 = 0 -18 + -2y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + -2y + 18 + y2 = 0 + 18 Reorder the terms: -18 + 18 + -2y + y2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -2y + y2 = 0 + 18 -2y + y2 = 0 + 18 Combine like terms: 0 + 18 = 18 -2y + y2 = 18 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 = 18 + 1 Reorder the terms: 1 + -2y + y2 = 18 + 1 Combine like terms: 18 + 1 = 19 1 + -2y + y2 = 19 Factor a perfect square on the left side: (y + -1)(y + -1) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (y + -1) equal to 4.358898944 and -4.358898944.Subproblem 1
y + -1 = 4.358898944 Simplifying y + -1 = 4.358898944 Reorder the terms: -1 + y = 4.358898944 Solving -1 + y = 4.358898944 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 = 4.358898944 + 1 Combine like terms: -1 + 1 = 0 0 + y = 4.358898944 + 1 y = 4.358898944 + 1 Combine like terms: 4.358898944 + 1 = 5.358898944 y = 5.358898944 Simplifying y = 5.358898944Subproblem 2
y + -1 = -4.358898944 Simplifying y + -1 = -4.358898944 Reorder the terms: -1 + y = -4.358898944 Solving -1 + y = -4.358898944 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 = -4.358898944 + 1 Combine like terms: -1 + 1 = 0 0 + y = -4.358898944 + 1 y = -4.358898944 + 1 Combine like terms: -4.358898944 + 1 = -3.358898944 y = -3.358898944 Simplifying y = -3.358898944Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.358898944, -3.358898944}
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