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Simplifying x2 + 11x + -140 = 0 Reorder the terms: -140 + 11x + x2 = 0 Solving -140 + 11x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '140' to each side of the equation. -140 + 11x + 140 + x2 = 0 + 140 Reorder the terms: -140 + 140 + 11x + x2 = 0 + 140 Combine like terms: -140 + 140 = 0 0 + 11x + x2 = 0 + 140 11x + x2 = 0 + 140 Combine like terms: 0 + 140 = 140 11x + x2 = 140 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 = 140 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 140 + 30.25 Combine like terms: 140 + 30.25 = 170.25 30.25 + 11x + x2 = 170.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 170.25 Calculate the square root of the right side: 13.047988351 Break this problem into two subproblems by setting (x + 5.5) equal to 13.047988351 and -13.047988351.Subproblem 1
x + 5.5 = 13.047988351 Simplifying x + 5.5 = 13.047988351 Reorder the terms: 5.5 + x = 13.047988351 Solving 5.5 + x = 13.047988351 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 = 13.047988351 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 13.047988351 + -5.5 x = 13.047988351 + -5.5 Combine like terms: 13.047988351 + -5.5 = 7.547988351 x = 7.547988351 Simplifying x = 7.547988351Subproblem 2
x + 5.5 = -13.047988351 Simplifying x + 5.5 = -13.047988351 Reorder the terms: 5.5 + x = -13.047988351 Solving 5.5 + x = -13.047988351 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 = -13.047988351 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -13.047988351 + -5.5 x = -13.047988351 + -5.5 Combine like terms: -13.047988351 + -5.5 = -18.547988351 x = -18.547988351 Simplifying x = -18.547988351Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.547988351, -18.547988351}
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