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Simplifying x(x + 5) = 207 Reorder the terms: x(5 + x) = 207 (5 * x + x * x) = 207 (5x + x2) = 207 Solving 5x + x2 = 207 Solving for variable 'x'. Reorder the terms: -207 + 5x + x2 = 207 + -207 Combine like terms: 207 + -207 = 0 -207 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '207' to each side of the equation. -207 + 5x + 207 + x2 = 0 + 207 Reorder the terms: -207 + 207 + 5x + x2 = 0 + 207 Combine like terms: -207 + 207 = 0 0 + 5x + x2 = 0 + 207 5x + x2 = 0 + 207 Combine like terms: 0 + 207 = 207 5x + x2 = 207 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 207 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 207 + 6.25 Combine like terms: 207 + 6.25 = 213.25 6.25 + 5x + x2 = 213.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 213.25 Calculate the square root of the right side: 14.603081867 Break this problem into two subproblems by setting (x + 2.5) equal to 14.603081867 and -14.603081867.Subproblem 1
x + 2.5 = 14.603081867 Simplifying x + 2.5 = 14.603081867 Reorder the terms: 2.5 + x = 14.603081867 Solving 2.5 + x = 14.603081867 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 14.603081867 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 14.603081867 + -2.5 x = 14.603081867 + -2.5 Combine like terms: 14.603081867 + -2.5 = 12.103081867 x = 12.103081867 Simplifying x = 12.103081867Subproblem 2
x + 2.5 = -14.603081867 Simplifying x + 2.5 = -14.603081867 Reorder the terms: 2.5 + x = -14.603081867 Solving 2.5 + x = -14.603081867 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -14.603081867 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -14.603081867 + -2.5 x = -14.603081867 + -2.5 Combine like terms: -14.603081867 + -2.5 = -17.103081867 x = -17.103081867 Simplifying x = -17.103081867Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.103081867, -17.103081867}
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