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Simplifying x2 + -1x = 125 Reorder the terms: -1x + x2 = 125 Solving -1x + x2 = 125 Solving for variable 'x'. Reorder the terms: -125 + -1x + x2 = 125 + -125 Combine like terms: 125 + -125 = 0 -125 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '125' to each side of the equation. -125 + -1x + 125 + x2 = 0 + 125 Reorder the terms: -125 + 125 + -1x + x2 = 0 + 125 Combine like terms: -125 + 125 = 0 0 + -1x + x2 = 0 + 125 -1x + x2 = 0 + 125 Combine like terms: 0 + 125 = 125 -1x + x2 = 125 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 125 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 125 + 0.25 Combine like terms: 125 + 0.25 = 125.25 0.25 + -1x + x2 = 125.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 125.25 Calculate the square root of the right side: 11.191514643 Break this problem into two subproblems by setting (x + -0.5) equal to 11.191514643 and -11.191514643.Subproblem 1
x + -0.5 = 11.191514643 Simplifying x + -0.5 = 11.191514643 Reorder the terms: -0.5 + x = 11.191514643 Solving -0.5 + x = 11.191514643 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 11.191514643 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 11.191514643 + 0.5 x = 11.191514643 + 0.5 Combine like terms: 11.191514643 + 0.5 = 11.691514643 x = 11.691514643 Simplifying x = 11.691514643Subproblem 2
x + -0.5 = -11.191514643 Simplifying x + -0.5 = -11.191514643 Reorder the terms: -0.5 + x = -11.191514643 Solving -0.5 + x = -11.191514643 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -11.191514643 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -11.191514643 + 0.5 x = -11.191514643 + 0.5 Combine like terms: -11.191514643 + 0.5 = -10.691514643 x = -10.691514643 Simplifying x = -10.691514643Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.691514643, -10.691514643}
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