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Simplifying x2 + -8x + -60 = -9 Reorder the terms: -60 + -8x + x2 = -9 Solving -60 + -8x + x2 = -9 Solving for variable 'x'. Reorder the terms: -60 + 9 + -8x + x2 = -9 + 9 Combine like terms: -60 + 9 = -51 -51 + -8x + x2 = -9 + 9 Combine like terms: -9 + 9 = 0 -51 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '51' to each side of the equation. -51 + -8x + 51 + x2 = 0 + 51 Reorder the terms: -51 + 51 + -8x + x2 = 0 + 51 Combine like terms: -51 + 51 = 0 0 + -8x + x2 = 0 + 51 -8x + x2 = 0 + 51 Combine like terms: 0 + 51 = 51 -8x + x2 = 51 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 51 + 16 Reorder the terms: 16 + -8x + x2 = 51 + 16 Combine like terms: 51 + 16 = 67 16 + -8x + x2 = 67 Factor a perfect square on the left side: (x + -4)(x + -4) = 67 Calculate the square root of the right side: 8.185352772 Break this problem into two subproblems by setting (x + -4) equal to 8.185352772 and -8.185352772.Subproblem 1
x + -4 = 8.185352772 Simplifying x + -4 = 8.185352772 Reorder the terms: -4 + x = 8.185352772 Solving -4 + x = 8.185352772 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 8.185352772 + 4 Combine like terms: -4 + 4 = 0 0 + x = 8.185352772 + 4 x = 8.185352772 + 4 Combine like terms: 8.185352772 + 4 = 12.185352772 x = 12.185352772 Simplifying x = 12.185352772Subproblem 2
x + -4 = -8.185352772 Simplifying x + -4 = -8.185352772 Reorder the terms: -4 + x = -8.185352772 Solving -4 + x = -8.185352772 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -8.185352772 + 4 Combine like terms: -4 + 4 = 0 0 + x = -8.185352772 + 4 x = -8.185352772 + 4 Combine like terms: -8.185352772 + 4 = -4.185352772 x = -4.185352772 Simplifying x = -4.185352772Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.185352772, -4.185352772}
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