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Simplifying y2 + -2y + -10 = 0 Reorder the terms: -10 + -2y + y2 = 0 Solving -10 + -2y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -2y + 10 + y2 = 0 + 10 Reorder the terms: -10 + 10 + -2y + y2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -2y + y2 = 0 + 10 -2y + y2 = 0 + 10 Combine like terms: 0 + 10 = 10 -2y + y2 = 10 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 = 10 + 1 Reorder the terms: 1 + -2y + y2 = 10 + 1 Combine like terms: 10 + 1 = 11 1 + -2y + y2 = 11 Factor a perfect square on the left side: (y + -1)(y + -1) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (y + -1) equal to 3.31662479 and -3.31662479.Subproblem 1
y + -1 = 3.31662479 Simplifying y + -1 = 3.31662479 Reorder the terms: -1 + y = 3.31662479 Solving -1 + y = 3.31662479 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 = 3.31662479 + 1 Combine like terms: -1 + 1 = 0 0 + y = 3.31662479 + 1 y = 3.31662479 + 1 Combine like terms: 3.31662479 + 1 = 4.31662479 y = 4.31662479 Simplifying y = 4.31662479Subproblem 2
y + -1 = -3.31662479 Simplifying y + -1 = -3.31662479 Reorder the terms: -1 + y = -3.31662479 Solving -1 + y = -3.31662479 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 = -3.31662479 + 1 Combine like terms: -1 + 1 = 0 0 + y = -3.31662479 + 1 y = -3.31662479 + 1 Combine like terms: -3.31662479 + 1 = -2.31662479 y = -2.31662479 Simplifying y = -2.31662479Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.31662479, -2.31662479}
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