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Simplifying 4x2 + -2x + -41 = 0 Reorder the terms: -41 + -2x + 4x2 = 0 Solving -41 + -2x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -10.25 + -0.5x + x2 = 0 Move the constant term to the right: Add '10.25' to each side of the equation. -10.25 + -0.5x + 10.25 + x2 = 0 + 10.25 Reorder the terms: -10.25 + 10.25 + -0.5x + x2 = 0 + 10.25 Combine like terms: -10.25 + 10.25 = 0.00 0.00 + -0.5x + x2 = 0 + 10.25 -0.5x + x2 = 0 + 10.25 Combine like terms: 0 + 10.25 = 10.25 -0.5x + x2 = 10.25 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 10.25 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 10.25 + 0.0625 Combine like terms: 10.25 + 0.0625 = 10.3125 0.0625 + -0.5x + x2 = 10.3125 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 10.3125 Calculate the square root of the right side: 3.211308145 Break this problem into two subproblems by setting (x + -0.25) equal to 3.211308145 and -3.211308145.Subproblem 1
x + -0.25 = 3.211308145 Simplifying x + -0.25 = 3.211308145 Reorder the terms: -0.25 + x = 3.211308145 Solving -0.25 + x = 3.211308145 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 3.211308145 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 3.211308145 + 0.25 x = 3.211308145 + 0.25 Combine like terms: 3.211308145 + 0.25 = 3.461308145 x = 3.461308145 Simplifying x = 3.461308145Subproblem 2
x + -0.25 = -3.211308145 Simplifying x + -0.25 = -3.211308145 Reorder the terms: -0.25 + x = -3.211308145 Solving -0.25 + x = -3.211308145 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -3.211308145 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -3.211308145 + 0.25 x = -3.211308145 + 0.25 Combine like terms: -3.211308145 + 0.25 = -2.961308145 x = -2.961308145 Simplifying x = -2.961308145Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.461308145, -2.961308145}
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