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Simplifying x2 + (x + 1) = 130 Reorder the terms: x2 + (1 + x) = 130 Remove parenthesis around (1 + x) x2 + 1 + x = 130 Reorder the terms: 1 + x + x2 = 130 Solving 1 + x + x2 = 130 Solving for variable 'x'. Reorder the terms: 1 + -130 + x + x2 = 130 + -130 Combine like terms: 1 + -130 = -129 -129 + x + x2 = 130 + -130 Combine like terms: 130 + -130 = 0 -129 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '129' to each side of the equation. -129 + x + 129 + x2 = 0 + 129 Reorder the terms: -129 + 129 + x + x2 = 0 + 129 Combine like terms: -129 + 129 = 0 0 + x + x2 = 0 + 129 x + x2 = 0 + 129 Combine like terms: 0 + 129 = 129 x + x2 = 129 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 = 129 + 0.25 Reorder the terms: 0.25 + x + x2 = 129 + 0.25 Combine like terms: 129 + 0.25 = 129.25 0.25 + x + x2 = 129.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 129.25 Calculate the square root of the right side: 11.368817001 Break this problem into two subproblems by setting (x + 0.5) equal to 11.368817001 and -11.368817001.Subproblem 1
x + 0.5 = 11.368817001 Simplifying x + 0.5 = 11.368817001 Reorder the terms: 0.5 + x = 11.368817001 Solving 0.5 + x = 11.368817001 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 = 11.368817001 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 11.368817001 + -0.5 x = 11.368817001 + -0.5 Combine like terms: 11.368817001 + -0.5 = 10.868817001 x = 10.868817001 Simplifying x = 10.868817001Subproblem 2
x + 0.5 = -11.368817001 Simplifying x + 0.5 = -11.368817001 Reorder the terms: 0.5 + x = -11.368817001 Solving 0.5 + x = -11.368817001 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 = -11.368817001 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -11.368817001 + -0.5 x = -11.368817001 + -0.5 Combine like terms: -11.368817001 + -0.5 = -11.868817001 x = -11.868817001 Simplifying x = -11.868817001Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.868817001, -11.868817001}
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