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Simplifying x(x + -1) = 13 Reorder the terms: x(-1 + x) = 13 (-1 * x + x * x) = 13 (-1x + x2) = 13 Solving -1x + x2 = 13 Solving for variable 'x'. Reorder the terms: -13 + -1x + x2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + -1x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + -1x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -1x + x2 = 0 + 13 -1x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 -1x + x2 = 13 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 = 13 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 13 + 0.25 Combine like terms: 13 + 0.25 = 13.25 0.25 + -1x + x2 = 13.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 13.25 Calculate the square root of the right side: 3.640054945 Break this problem into two subproblems by setting (x + -0.5) equal to 3.640054945 and -3.640054945.Subproblem 1
x + -0.5 = 3.640054945 Simplifying x + -0.5 = 3.640054945 Reorder the terms: -0.5 + x = 3.640054945 Solving -0.5 + x = 3.640054945 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 = 3.640054945 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 3.640054945 + 0.5 x = 3.640054945 + 0.5 Combine like terms: 3.640054945 + 0.5 = 4.140054945 x = 4.140054945 Simplifying x = 4.140054945Subproblem 2
x + -0.5 = -3.640054945 Simplifying x + -0.5 = -3.640054945 Reorder the terms: -0.5 + x = -3.640054945 Solving -0.5 + x = -3.640054945 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 = -3.640054945 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -3.640054945 + 0.5 x = -3.640054945 + 0.5 Combine like terms: -3.640054945 + 0.5 = -3.140054945 x = -3.140054945 Simplifying x = -3.140054945Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.140054945, -3.140054945}
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