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Simplifying x2 + 11x + -1000 = 0 Reorder the terms: -1000 + 11x + x2 = 0 Solving -1000 + 11x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1000' to each side of the equation. -1000 + 11x + 1000 + x2 = 0 + 1000 Reorder the terms: -1000 + 1000 + 11x + x2 = 0 + 1000 Combine like terms: -1000 + 1000 = 0 0 + 11x + x2 = 0 + 1000 11x + x2 = 0 + 1000 Combine like terms: 0 + 1000 = 1000 11x + x2 = 1000 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 = 1000 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 1000 + 30.25 Combine like terms: 1000 + 30.25 = 1030.25 30.25 + 11x + x2 = 1030.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 1030.25 Calculate the square root of the right side: 32.097507691 Break this problem into two subproblems by setting (x + 5.5) equal to 32.097507691 and -32.097507691.Subproblem 1
x + 5.5 = 32.097507691 Simplifying x + 5.5 = 32.097507691 Reorder the terms: 5.5 + x = 32.097507691 Solving 5.5 + x = 32.097507691 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 = 32.097507691 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 32.097507691 + -5.5 x = 32.097507691 + -5.5 Combine like terms: 32.097507691 + -5.5 = 26.597507691 x = 26.597507691 Simplifying x = 26.597507691Subproblem 2
x + 5.5 = -32.097507691 Simplifying x + 5.5 = -32.097507691 Reorder the terms: 5.5 + x = -32.097507691 Solving 5.5 + x = -32.097507691 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 = -32.097507691 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -32.097507691 + -5.5 x = -32.097507691 + -5.5 Combine like terms: -32.097507691 + -5.5 = -37.597507691 x = -37.597507691 Simplifying x = -37.597507691Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.597507691, -37.597507691}
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