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Simplifying (x) = x2 + -10x + -3 x = x2 + -10x + -3 Reorder the terms: x = -3 + -10x + x2 Solving x = -3 + -10x + x2 Solving for variable 'x'. Reorder the terms: 3 + x + 10x + -1x2 = -3 + -10x + x2 + 3 + 10x + -1x2 Combine like terms: x + 10x = 11x 3 + 11x + -1x2 = -3 + -10x + x2 + 3 + 10x + -1x2 Reorder the terms: 3 + 11x + -1x2 = -3 + 3 + -10x + 10x + x2 + -1x2 Combine like terms: -3 + 3 = 0 3 + 11x + -1x2 = 0 + -10x + 10x + x2 + -1x2 3 + 11x + -1x2 = -10x + 10x + x2 + -1x2 Combine like terms: -10x + 10x = 0 3 + 11x + -1x2 = 0 + x2 + -1x2 3 + 11x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 3 + 11x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3 + -11x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -11x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -11x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -11x + x2 = 0 + 3 -11x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -11x + x2 = 3 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 = 3 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 3 + 30.25 Combine like terms: 3 + 30.25 = 33.25 30.25 + -11x + x2 = 33.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 33.25 Calculate the square root of the right side: 5.766281297 Break this problem into two subproblems by setting (x + -5.5) equal to 5.766281297 and -5.766281297.Subproblem 1
x + -5.5 = 5.766281297 Simplifying x + -5.5 = 5.766281297 Reorder the terms: -5.5 + x = 5.766281297 Solving -5.5 + x = 5.766281297 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 = 5.766281297 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 5.766281297 + 5.5 x = 5.766281297 + 5.5 Combine like terms: 5.766281297 + 5.5 = 11.266281297 x = 11.266281297 Simplifying x = 11.266281297Subproblem 2
x + -5.5 = -5.766281297 Simplifying x + -5.5 = -5.766281297 Reorder the terms: -5.5 + x = -5.766281297 Solving -5.5 + x = -5.766281297 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 = -5.766281297 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -5.766281297 + 5.5 x = -5.766281297 + 5.5 Combine like terms: -5.766281297 + 5.5 = -0.266281297 x = -0.266281297 Simplifying x = -0.266281297Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.266281297, -0.266281297}
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