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Simplifying x(x + 1) = 1035 Reorder the terms: x(1 + x) = 1035 (1 * x + x * x) = 1035 (1x + x2) = 1035 Solving 1x + x2 = 1035 Solving for variable 'x'. Reorder the terms: -1035 + 1x + x2 = 1035 + -1035 Combine like terms: 1035 + -1035 = 0 -1035 + 1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1035' to each side of the equation. -1035 + 1x + 1035 + x2 = 0 + 1035 Reorder the terms: -1035 + 1035 + 1x + x2 = 0 + 1035 Combine like terms: -1035 + 1035 = 0 0 + 1x + x2 = 0 + 1035 1x + x2 = 0 + 1035 Combine like terms: 0 + 1035 = 1035 1x + x2 = 1035 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. x + 0.25 + x2 = 1035 + 0.25 Reorder the terms: 0.25 + x + x2 = 1035 + 0.25 Combine like terms: 1035 + 0.25 = 1035.25 0.25 + x + x2 = 1035.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 1035.25 Calculate the square root of the right side: 32.175301086 Break this problem into two subproblems by setting (x + 0.5) equal to 32.175301086 and -32.175301086.Subproblem 1
x + 0.5 = 32.175301086 Simplifying x + 0.5 = 32.175301086 Reorder the terms: 0.5 + x = 32.175301086 Solving 0.5 + x = 32.175301086 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 = 32.175301086 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 32.175301086 + -0.5 x = 32.175301086 + -0.5 Combine like terms: 32.175301086 + -0.5 = 31.675301086 x = 31.675301086 Simplifying x = 31.675301086Subproblem 2
x + 0.5 = -32.175301086 Simplifying x + 0.5 = -32.175301086 Reorder the terms: 0.5 + x = -32.175301086 Solving 0.5 + x = -32.175301086 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 = -32.175301086 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -32.175301086 + -0.5 x = -32.175301086 + -0.5 Combine like terms: -32.175301086 + -0.5 = -32.675301086 x = -32.675301086 Simplifying x = -32.675301086Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.675301086, -32.675301086}
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