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Simplifying x * x + x = 65 Multiply x * x x2 + x = 65 Reorder the terms: x + x2 = 65 Solving x + x2 = 65 Solving for variable 'x'. Reorder the terms: -65 + x + x2 = 65 + -65 Combine like terms: 65 + -65 = 0 -65 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '65' to each side of the equation. -65 + x + 65 + x2 = 0 + 65 Reorder the terms: -65 + 65 + x + x2 = 0 + 65 Combine like terms: -65 + 65 = 0 0 + x + x2 = 0 + 65 x + x2 = 0 + 65 Combine like terms: 0 + 65 = 65 x + x2 = 65 The x term is x. 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. x + 0.25 + x2 = 65 + 0.25 Reorder the terms: 0.25 + x + x2 = 65 + 0.25 Combine like terms: 65 + 0.25 = 65.25 0.25 + x + x2 = 65.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 65.25 Calculate the square root of the right side: 8.077747211 Break this problem into two subproblems by setting (x + 0.5) equal to 8.077747211 and -8.077747211.Subproblem 1
x + 0.5 = 8.077747211 Simplifying x + 0.5 = 8.077747211 Reorder the terms: 0.5 + x = 8.077747211 Solving 0.5 + x = 8.077747211 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 = 8.077747211 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 8.077747211 + -0.5 x = 8.077747211 + -0.5 Combine like terms: 8.077747211 + -0.5 = 7.577747211 x = 7.577747211 Simplifying x = 7.577747211Subproblem 2
x + 0.5 = -8.077747211 Simplifying x + 0.5 = -8.077747211 Reorder the terms: 0.5 + x = -8.077747211 Solving 0.5 + x = -8.077747211 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 = -8.077747211 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -8.077747211 + -0.5 x = -8.077747211 + -0.5 Combine like terms: -8.077747211 + -0.5 = -8.577747211 x = -8.577747211 Simplifying x = -8.577747211Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.577747211, -8.577747211}
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