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Simplifying x2 + -1x + 0.25 = 11 Reorder the terms: 0.25 + -1x + x2 = 11 Solving 0.25 + -1x + x2 = 11 Solving for variable 'x'. Reorder the terms: 0.25 + -11 + -1x + x2 = 11 + -11 Combine like terms: 0.25 + -11 = -10.75 -10.75 + -1x + x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -10.75 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '10.75' to each side of the equation. -10.75 + -1x + 10.75 + x2 = 0 + 10.75 Reorder the terms: -10.75 + 10.75 + -1x + x2 = 0 + 10.75 Combine like terms: -10.75 + 10.75 = 0.00 0.00 + -1x + x2 = 0 + 10.75 -1x + x2 = 0 + 10.75 Combine like terms: 0 + 10.75 = 10.75 -1x + x2 = 10.75 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 10.75 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 10.75 + 0.25 Combine like terms: 10.75 + 0.25 = 11 0.25 + -1x + x2 = 11 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (x + -0.5) equal to 3.31662479 and -3.31662479.Subproblem 1
x + -0.5 = 3.31662479 Simplifying x + -0.5 = 3.31662479 Reorder the terms: -0.5 + x = 3.31662479 Solving -0.5 + x = 3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 3.31662479 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 3.31662479 + 0.5 x = 3.31662479 + 0.5 Combine like terms: 3.31662479 + 0.5 = 3.81662479 x = 3.81662479 Simplifying x = 3.81662479Subproblem 2
x + -0.5 = -3.31662479 Simplifying x + -0.5 = -3.31662479 Reorder the terms: -0.5 + x = -3.31662479 Solving -0.5 + x = -3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -3.31662479 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -3.31662479 + 0.5 x = -3.31662479 + 0.5 Combine like terms: -3.31662479 + 0.5 = -2.81662479 x = -2.81662479 Simplifying x = -2.81662479Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.81662479, -2.81662479}
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