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Simplifying x2 + -10x + -168 = 0 Reorder the terms: -168 + -10x + x2 = 0 Solving -168 + -10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '168' to each side of the equation. -168 + -10x + 168 + x2 = 0 + 168 Reorder the terms: -168 + 168 + -10x + x2 = 0 + 168 Combine like terms: -168 + 168 = 0 0 + -10x + x2 = 0 + 168 -10x + x2 = 0 + 168 Combine like terms: 0 + 168 = 168 -10x + x2 = 168 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 168 + 25 Reorder the terms: 25 + -10x + x2 = 168 + 25 Combine like terms: 168 + 25 = 193 25 + -10x + x2 = 193 Factor a perfect square on the left side: (x + -5)(x + -5) = 193 Calculate the square root of the right side: 13.892443989 Break this problem into two subproblems by setting (x + -5) equal to 13.892443989 and -13.892443989.Subproblem 1
x + -5 = 13.892443989 Simplifying x + -5 = 13.892443989 Reorder the terms: -5 + x = 13.892443989 Solving -5 + x = 13.892443989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 13.892443989 + 5 Combine like terms: -5 + 5 = 0 0 + x = 13.892443989 + 5 x = 13.892443989 + 5 Combine like terms: 13.892443989 + 5 = 18.892443989 x = 18.892443989 Simplifying x = 18.892443989Subproblem 2
x + -5 = -13.892443989 Simplifying x + -5 = -13.892443989 Reorder the terms: -5 + x = -13.892443989 Solving -5 + x = -13.892443989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -13.892443989 + 5 Combine like terms: -5 + 5 = 0 0 + x = -13.892443989 + 5 x = -13.892443989 + 5 Combine like terms: -13.892443989 + 5 = -8.892443989 x = -8.892443989 Simplifying x = -8.892443989Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.892443989, -8.892443989}
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