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Simplifying 11x2 + 55x + -13000 = 0 Reorder the terms: -13000 + 55x + 11x2 = 0 Solving -13000 + 55x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -1181.818182 + 5x + x2 = 0 Move the constant term to the right: Add '1181.818182' to each side of the equation. -1181.818182 + 5x + 1181.818182 + x2 = 0 + 1181.818182 Reorder the terms: -1181.818182 + 1181.818182 + 5x + x2 = 0 + 1181.818182 Combine like terms: -1181.818182 + 1181.818182 = 0.000000 0.000000 + 5x + x2 = 0 + 1181.818182 5x + x2 = 0 + 1181.818182 Combine like terms: 0 + 1181.818182 = 1181.818182 5x + x2 = 1181.818182 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 1181.818182 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 1181.818182 + 6.25 Combine like terms: 1181.818182 + 6.25 = 1188.068182 6.25 + 5x + x2 = 1188.068182 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 1188.068182 Calculate the square root of the right side: 34.468364945 Break this problem into two subproblems by setting (x + 2.5) equal to 34.468364945 and -34.468364945.Subproblem 1
x + 2.5 = 34.468364945 Simplifying x + 2.5 = 34.468364945 Reorder the terms: 2.5 + x = 34.468364945 Solving 2.5 + x = 34.468364945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 34.468364945 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 34.468364945 + -2.5 x = 34.468364945 + -2.5 Combine like terms: 34.468364945 + -2.5 = 31.968364945 x = 31.968364945 Simplifying x = 31.968364945Subproblem 2
x + 2.5 = -34.468364945 Simplifying x + 2.5 = -34.468364945 Reorder the terms: 2.5 + x = -34.468364945 Solving 2.5 + x = -34.468364945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -34.468364945 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -34.468364945 + -2.5 x = -34.468364945 + -2.5 Combine like terms: -34.468364945 + -2.5 = -36.968364945 x = -36.968364945 Simplifying x = -36.968364945Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.968364945, -36.968364945}
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