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Simplifying x2 + -11x + -3 = 5 Reorder the terms: -3 + -11x + x2 = 5 Solving -3 + -11x + x2 = 5 Solving for variable 'x'. Reorder the terms: -3 + -5 + -11x + x2 = 5 + -5 Combine like terms: -3 + -5 = -8 -8 + -11x + x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -8 + -11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -11x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -11x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -11x + x2 = 0 + 8 -11x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -11x + x2 = 8 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 = 8 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 8 + 30.25 Combine like terms: 8 + 30.25 = 38.25 30.25 + -11x + x2 = 38.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 38.25 Calculate the square root of the right side: 6.184658438 Break this problem into two subproblems by setting (x + -5.5) equal to 6.184658438 and -6.184658438.Subproblem 1
x + -5.5 = 6.184658438 Simplifying x + -5.5 = 6.184658438 Reorder the terms: -5.5 + x = 6.184658438 Solving -5.5 + x = 6.184658438 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 = 6.184658438 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 6.184658438 + 5.5 x = 6.184658438 + 5.5 Combine like terms: 6.184658438 + 5.5 = 11.684658438 x = 11.684658438 Simplifying x = 11.684658438Subproblem 2
x + -5.5 = -6.184658438 Simplifying x + -5.5 = -6.184658438 Reorder the terms: -5.5 + x = -6.184658438 Solving -5.5 + x = -6.184658438 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 = -6.184658438 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -6.184658438 + 5.5 x = -6.184658438 + 5.5 Combine like terms: -6.184658438 + 5.5 = -0.684658438 x = -0.684658438 Simplifying x = -0.684658438Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.684658438, -0.684658438}
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