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Simplifying x2 + -10x + -125 = 14 Reorder the terms: -125 + -10x + x2 = 14 Solving -125 + -10x + x2 = 14 Solving for variable 'x'. Reorder the terms: -125 + -14 + -10x + x2 = 14 + -14 Combine like terms: -125 + -14 = -139 -139 + -10x + x2 = 14 + -14 Combine like terms: 14 + -14 = 0 -139 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '139' to each side of the equation. -139 + -10x + 139 + x2 = 0 + 139 Reorder the terms: -139 + 139 + -10x + x2 = 0 + 139 Combine like terms: -139 + 139 = 0 0 + -10x + x2 = 0 + 139 -10x + x2 = 0 + 139 Combine like terms: 0 + 139 = 139 -10x + x2 = 139 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 = 139 + 25 Reorder the terms: 25 + -10x + x2 = 139 + 25 Combine like terms: 139 + 25 = 164 25 + -10x + x2 = 164 Factor a perfect square on the left side: (x + -5)(x + -5) = 164 Calculate the square root of the right side: 12.806248475 Break this problem into two subproblems by setting (x + -5) equal to 12.806248475 and -12.806248475.Subproblem 1
x + -5 = 12.806248475 Simplifying x + -5 = 12.806248475 Reorder the terms: -5 + x = 12.806248475 Solving -5 + x = 12.806248475 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 = 12.806248475 + 5 Combine like terms: -5 + 5 = 0 0 + x = 12.806248475 + 5 x = 12.806248475 + 5 Combine like terms: 12.806248475 + 5 = 17.806248475 x = 17.806248475 Simplifying x = 17.806248475Subproblem 2
x + -5 = -12.806248475 Simplifying x + -5 = -12.806248475 Reorder the terms: -5 + x = -12.806248475 Solving -5 + x = -12.806248475 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 = -12.806248475 + 5 Combine like terms: -5 + 5 = 0 0 + x = -12.806248475 + 5 x = -12.806248475 + 5 Combine like terms: -12.806248475 + 5 = -7.806248475 x = -7.806248475 Simplifying x = -7.806248475Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.806248475, -7.806248475}
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