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Simplifying x(x + 5) = 201 Reorder the terms: x(5 + x) = 201 (5 * x + x * x) = 201 (5x + x2) = 201 Solving 5x + x2 = 201 Solving for variable 'x'. Reorder the terms: -201 + 5x + x2 = 201 + -201 Combine like terms: 201 + -201 = 0 -201 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '201' to each side of the equation. -201 + 5x + 201 + x2 = 0 + 201 Reorder the terms: -201 + 201 + 5x + x2 = 0 + 201 Combine like terms: -201 + 201 = 0 0 + 5x + x2 = 0 + 201 5x + x2 = 0 + 201 Combine like terms: 0 + 201 = 201 5x + x2 = 201 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 = 201 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 201 + 6.25 Combine like terms: 201 + 6.25 = 207.25 6.25 + 5x + x2 = 207.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 207.25 Calculate the square root of the right side: 14.396180049 Break this problem into two subproblems by setting (x + 2.5) equal to 14.396180049 and -14.396180049.Subproblem 1
x + 2.5 = 14.396180049 Simplifying x + 2.5 = 14.396180049 Reorder the terms: 2.5 + x = 14.396180049 Solving 2.5 + x = 14.396180049 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 = 14.396180049 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 14.396180049 + -2.5 x = 14.396180049 + -2.5 Combine like terms: 14.396180049 + -2.5 = 11.896180049 x = 11.896180049 Simplifying x = 11.896180049Subproblem 2
x + 2.5 = -14.396180049 Simplifying x + 2.5 = -14.396180049 Reorder the terms: 2.5 + x = -14.396180049 Solving 2.5 + x = -14.396180049 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 = -14.396180049 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -14.396180049 + -2.5 x = -14.396180049 + -2.5 Combine like terms: -14.396180049 + -2.5 = -16.896180049 x = -16.896180049 Simplifying x = -16.896180049Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.896180049, -16.896180049}
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