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Simplifying 11x2 + -600x + -2890 = 0 Reorder the terms: -2890 + -600x + 11x2 = 0 Solving -2890 + -600x + 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'. -262.7272727 + -54.54545455x + x2 = 0 Move the constant term to the right: Add '262.7272727' to each side of the equation. -262.7272727 + -54.54545455x + 262.7272727 + x2 = 0 + 262.7272727 Reorder the terms: -262.7272727 + 262.7272727 + -54.54545455x + x2 = 0 + 262.7272727 Combine like terms: -262.7272727 + 262.7272727 = 0.0000000 0.0000000 + -54.54545455x + x2 = 0 + 262.7272727 -54.54545455x + x2 = 0 + 262.7272727 Combine like terms: 0 + 262.7272727 = 262.7272727 -54.54545455x + x2 = 262.7272727 The x term is -54.54545455x. Take half its coefficient (-27.27272728). Square it (743.8016533) and add it to both sides. Add '743.8016533' to each side of the equation. -54.54545455x + 743.8016533 + x2 = 262.7272727 + 743.8016533 Reorder the terms: 743.8016533 + -54.54545455x + x2 = 262.7272727 + 743.8016533 Combine like terms: 262.7272727 + 743.8016533 = 1006.528926 743.8016533 + -54.54545455x + x2 = 1006.528926 Factor a perfect square on the left side: (x + -27.27272728)(x + -27.27272728) = 1006.528926 Calculate the square root of the right side: 31.725840036 Break this problem into two subproblems by setting (x + -27.27272728) equal to 31.725840036 and -31.725840036.Subproblem 1
x + -27.27272728 = 31.725840036 Simplifying x + -27.27272728 = 31.725840036 Reorder the terms: -27.27272728 + x = 31.725840036 Solving -27.27272728 + x = 31.725840036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27.27272728' to each side of the equation. -27.27272728 + 27.27272728 + x = 31.725840036 + 27.27272728 Combine like terms: -27.27272728 + 27.27272728 = 0.00000000 0.00000000 + x = 31.725840036 + 27.27272728 x = 31.725840036 + 27.27272728 Combine like terms: 31.725840036 + 27.27272728 = 58.998567316 x = 58.998567316 Simplifying x = 58.998567316Subproblem 2
x + -27.27272728 = -31.725840036 Simplifying x + -27.27272728 = -31.725840036 Reorder the terms: -27.27272728 + x = -31.725840036 Solving -27.27272728 + x = -31.725840036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27.27272728' to each side of the equation. -27.27272728 + 27.27272728 + x = -31.725840036 + 27.27272728 Combine like terms: -27.27272728 + 27.27272728 = 0.00000000 0.00000000 + x = -31.725840036 + 27.27272728 x = -31.725840036 + 27.27272728 Combine like terms: -31.725840036 + 27.27272728 = -4.453112756 x = -4.453112756 Simplifying x = -4.453112756Solution
The solution to the problem is based on the solutions from the subproblems. x = {58.998567316, -4.453112756}
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