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Simplifying 4x2 + -13x + 1 = 0 Reorder the terms: 1 + -13x + 4x2 = 0 Solving 1 + -13x + 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'. 0.25 + -3.25x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -3.25x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -3.25x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -3.25x + x2 = 0 + -0.25 -3.25x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -3.25x + x2 = -0.25 The x term is -3.25x. Take half its coefficient (-1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. -3.25x + 2.640625 + x2 = -0.25 + 2.640625 Reorder the terms: 2.640625 + -3.25x + x2 = -0.25 + 2.640625 Combine like terms: -0.25 + 2.640625 = 2.390625 2.640625 + -3.25x + x2 = 2.390625 Factor a perfect square on the left side: (x + -1.625)(x + -1.625) = 2.390625 Calculate the square root of the right side: 1.54616461 Break this problem into two subproblems by setting (x + -1.625) equal to 1.54616461 and -1.54616461.Subproblem 1
x + -1.625 = 1.54616461 Simplifying x + -1.625 = 1.54616461 Reorder the terms: -1.625 + x = 1.54616461 Solving -1.625 + x = 1.54616461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + x = 1.54616461 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = 1.54616461 + 1.625 x = 1.54616461 + 1.625 Combine like terms: 1.54616461 + 1.625 = 3.17116461 x = 3.17116461 Simplifying x = 3.17116461Subproblem 2
x + -1.625 = -1.54616461 Simplifying x + -1.625 = -1.54616461 Reorder the terms: -1.625 + x = -1.54616461 Solving -1.625 + x = -1.54616461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + x = -1.54616461 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = -1.54616461 + 1.625 x = -1.54616461 + 1.625 Combine like terms: -1.54616461 + 1.625 = 0.07883539 x = 0.07883539 Simplifying x = 0.07883539Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.17116461, 0.07883539}
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