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Simplifying x2 + 105x + 1200 = 0 Reorder the terms: 1200 + 105x + x2 = 0 Solving 1200 + 105x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1200' to each side of the equation. 1200 + 105x + -1200 + x2 = 0 + -1200 Reorder the terms: 1200 + -1200 + 105x + x2 = 0 + -1200 Combine like terms: 1200 + -1200 = 0 0 + 105x + x2 = 0 + -1200 105x + x2 = 0 + -1200 Combine like terms: 0 + -1200 = -1200 105x + x2 = -1200 The x term is 105x. Take half its coefficient (52.5). Square it (2756.25) and add it to both sides. Add '2756.25' to each side of the equation. 105x + 2756.25 + x2 = -1200 + 2756.25 Reorder the terms: 2756.25 + 105x + x2 = -1200 + 2756.25 Combine like terms: -1200 + 2756.25 = 1556.25 2756.25 + 105x + x2 = 1556.25 Factor a perfect square on the left side: (x + 52.5)(x + 52.5) = 1556.25 Calculate the square root of the right side: 39.449334595 Break this problem into two subproblems by setting (x + 52.5) equal to 39.449334595 and -39.449334595.Subproblem 1
x + 52.5 = 39.449334595 Simplifying x + 52.5 = 39.449334595 Reorder the terms: 52.5 + x = 39.449334595 Solving 52.5 + x = 39.449334595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-52.5' to each side of the equation. 52.5 + -52.5 + x = 39.449334595 + -52.5 Combine like terms: 52.5 + -52.5 = 0.0 0.0 + x = 39.449334595 + -52.5 x = 39.449334595 + -52.5 Combine like terms: 39.449334595 + -52.5 = -13.050665405 x = -13.050665405 Simplifying x = -13.050665405Subproblem 2
x + 52.5 = -39.449334595 Simplifying x + 52.5 = -39.449334595 Reorder the terms: 52.5 + x = -39.449334595 Solving 52.5 + x = -39.449334595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-52.5' to each side of the equation. 52.5 + -52.5 + x = -39.449334595 + -52.5 Combine like terms: 52.5 + -52.5 = 0.0 0.0 + x = -39.449334595 + -52.5 x = -39.449334595 + -52.5 Combine like terms: -39.449334595 + -52.5 = -91.949334595 x = -91.949334595 Simplifying x = -91.949334595Solution
The solution to the problem is based on the solutions from the subproblems. x = {-13.050665405, -91.949334595}
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