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Simplifying y2 + -12y + -63 = 0 Reorder the terms: -63 + -12y + y2 = 0 Solving -63 + -12y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '63' to each side of the equation. -63 + -12y + 63 + y2 = 0 + 63 Reorder the terms: -63 + 63 + -12y + y2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + -12y + y2 = 0 + 63 -12y + y2 = 0 + 63 Combine like terms: 0 + 63 = 63 -12y + y2 = 63 The y term is -12y. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12y + 36 + y2 = 63 + 36 Reorder the terms: 36 + -12y + y2 = 63 + 36 Combine like terms: 63 + 36 = 99 36 + -12y + y2 = 99 Factor a perfect square on the left side: (y + -6)(y + -6) = 99 Calculate the square root of the right side: 9.949874371 Break this problem into two subproblems by setting (y + -6) equal to 9.949874371 and -9.949874371.Subproblem 1
y + -6 = 9.949874371 Simplifying y + -6 = 9.949874371 Reorder the terms: -6 + y = 9.949874371 Solving -6 + y = 9.949874371 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y = 9.949874371 + 6 Combine like terms: -6 + 6 = 0 0 + y = 9.949874371 + 6 y = 9.949874371 + 6 Combine like terms: 9.949874371 + 6 = 15.949874371 y = 15.949874371 Simplifying y = 15.949874371Subproblem 2
y + -6 = -9.949874371 Simplifying y + -6 = -9.949874371 Reorder the terms: -6 + y = -9.949874371 Solving -6 + y = -9.949874371 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y = -9.949874371 + 6 Combine like terms: -6 + 6 = 0 0 + y = -9.949874371 + 6 y = -9.949874371 + 6 Combine like terms: -9.949874371 + 6 = -3.949874371 y = -3.949874371 Simplifying y = -3.949874371Solution
The solution to the problem is based on the solutions from the subproblems. y = {15.949874371, -3.949874371}
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