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Simplifying x2 + -1x + -365 = 0 Reorder the terms: -365 + -1x + x2 = 0 Solving -365 + -1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '365' to each side of the equation. -365 + -1x + 365 + x2 = 0 + 365 Reorder the terms: -365 + 365 + -1x + x2 = 0 + 365 Combine like terms: -365 + 365 = 0 0 + -1x + x2 = 0 + 365 -1x + x2 = 0 + 365 Combine like terms: 0 + 365 = 365 -1x + x2 = 365 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. -1x + 0.25 + x2 = 365 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 365 + 0.25 Combine like terms: 365 + 0.25 = 365.25 0.25 + -1x + x2 = 365.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 365.25 Calculate the square root of the right side: 19.111514854 Break this problem into two subproblems by setting (x + -0.5) equal to 19.111514854 and -19.111514854.Subproblem 1
x + -0.5 = 19.111514854 Simplifying x + -0.5 = 19.111514854 Reorder the terms: -0.5 + x = 19.111514854 Solving -0.5 + x = 19.111514854 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 = 19.111514854 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 19.111514854 + 0.5 x = 19.111514854 + 0.5 Combine like terms: 19.111514854 + 0.5 = 19.611514854 x = 19.611514854 Simplifying x = 19.611514854Subproblem 2
x + -0.5 = -19.111514854 Simplifying x + -0.5 = -19.111514854 Reorder the terms: -0.5 + x = -19.111514854 Solving -0.5 + x = -19.111514854 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 = -19.111514854 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -19.111514854 + 0.5 x = -19.111514854 + 0.5 Combine like terms: -19.111514854 + 0.5 = -18.611514854 x = -18.611514854 Simplifying x = -18.611514854Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.611514854, -18.611514854}
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