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Simplifying (x2) + -113x + -186 = 0 x2 + -113x + -186 = 0 Reorder the terms: -186 + -113x + x2 = 0 Solving -186 + -113x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '186' to each side of the equation. -186 + -113x + 186 + x2 = 0 + 186 Reorder the terms: -186 + 186 + -113x + x2 = 0 + 186 Combine like terms: -186 + 186 = 0 0 + -113x + x2 = 0 + 186 -113x + x2 = 0 + 186 Combine like terms: 0 + 186 = 186 -113x + x2 = 186 The x term is -113x. Take half its coefficient (-56.5). Square it (3192.25) and add it to both sides. Add '3192.25' to each side of the equation. -113x + 3192.25 + x2 = 186 + 3192.25 Reorder the terms: 3192.25 + -113x + x2 = 186 + 3192.25 Combine like terms: 186 + 3192.25 = 3378.25 3192.25 + -113x + x2 = 3378.25 Factor a perfect square on the left side: (x + -56.5)(x + -56.5) = 3378.25 Calculate the square root of the right side: 58.122715009 Break this problem into two subproblems by setting (x + -56.5) equal to 58.122715009 and -58.122715009.Subproblem 1
x + -56.5 = 58.122715009 Simplifying x + -56.5 = 58.122715009 Reorder the terms: -56.5 + x = 58.122715009 Solving -56.5 + x = 58.122715009 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '56.5' to each side of the equation. -56.5 + 56.5 + x = 58.122715009 + 56.5 Combine like terms: -56.5 + 56.5 = 0.0 0.0 + x = 58.122715009 + 56.5 x = 58.122715009 + 56.5 Combine like terms: 58.122715009 + 56.5 = 114.622715009 x = 114.622715009 Simplifying x = 114.622715009Subproblem 2
x + -56.5 = -58.122715009 Simplifying x + -56.5 = -58.122715009 Reorder the terms: -56.5 + x = -58.122715009 Solving -56.5 + x = -58.122715009 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '56.5' to each side of the equation. -56.5 + 56.5 + x = -58.122715009 + 56.5 Combine like terms: -56.5 + 56.5 = 0.0 0.0 + x = -58.122715009 + 56.5 x = -58.122715009 + 56.5 Combine like terms: -58.122715009 + 56.5 = -1.622715009 x = -1.622715009 Simplifying x = -1.622715009Solution
The solution to the problem is based on the solutions from the subproblems. x = {114.622715009, -1.622715009}
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