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Simplifying x2 + 11x + -105 = 0 Reorder the terms: -105 + 11x + x2 = 0 Solving -105 + 11x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '105' to each side of the equation. -105 + 11x + 105 + x2 = 0 + 105 Reorder the terms: -105 + 105 + 11x + x2 = 0 + 105 Combine like terms: -105 + 105 = 0 0 + 11x + x2 = 0 + 105 11x + x2 = 0 + 105 Combine like terms: 0 + 105 = 105 11x + x2 = 105 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = 105 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 105 + 30.25 Combine like terms: 105 + 30.25 = 135.25 30.25 + 11x + x2 = 135.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 135.25 Calculate the square root of the right side: 11.62970335 Break this problem into two subproblems by setting (x + 5.5) equal to 11.62970335 and -11.62970335.Subproblem 1
x + 5.5 = 11.62970335 Simplifying x + 5.5 = 11.62970335 Reorder the terms: 5.5 + x = 11.62970335 Solving 5.5 + x = 11.62970335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 11.62970335 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 11.62970335 + -5.5 x = 11.62970335 + -5.5 Combine like terms: 11.62970335 + -5.5 = 6.12970335 x = 6.12970335 Simplifying x = 6.12970335Subproblem 2
x + 5.5 = -11.62970335 Simplifying x + 5.5 = -11.62970335 Reorder the terms: 5.5 + x = -11.62970335 Solving 5.5 + x = -11.62970335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -11.62970335 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -11.62970335 + -5.5 x = -11.62970335 + -5.5 Combine like terms: -11.62970335 + -5.5 = -17.12970335 x = -17.12970335 Simplifying x = -17.12970335Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.12970335, -17.12970335}
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