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Simplifying 38.75x2 + -43.3999x + 0.04806 = 0 Reorder the terms: 0.04806 + -43.3999x + 38.75x2 = 0 Solving 0.04806 + -43.3999x + 38.75x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 38.75 the coefficient of the squared term: Divide each side by '38.75'. 0.001240258065 + -1.119997419x + x2 = 0 Move the constant term to the right: Add '-0.001240258065' to each side of the equation. 0.001240258065 + -1.119997419x + -0.001240258065 + x2 = 0 + -0.001240258065 Reorder the terms: 0.001240258065 + -0.001240258065 + -1.119997419x + x2 = 0 + -0.001240258065 Combine like terms: 0.001240258065 + -0.001240258065 = 0.000000000000 0.000000000000 + -1.119997419x + x2 = 0 + -0.001240258065 -1.119997419x + x2 = 0 + -0.001240258065 Combine like terms: 0 + -0.001240258065 = -0.001240258065 -1.119997419x + x2 = -0.001240258065 The x term is -1.119997419x. Take half its coefficient (-0.5599987095). Square it (0.3135985546) and add it to both sides. Add '0.3135985546' to each side of the equation. -1.119997419x + 0.3135985546 + x2 = -0.001240258065 + 0.3135985546 Reorder the terms: 0.3135985546 + -1.119997419x + x2 = -0.001240258065 + 0.3135985546 Combine like terms: -0.001240258065 + 0.3135985546 = 0.312358296535 0.3135985546 + -1.119997419x + x2 = 0.312358296535 Factor a perfect square on the left side: (x + -0.5599987095)(x + -0.5599987095) = 0.312358296535 Calculate the square root of the right side: 0.558890237 Break this problem into two subproblems by setting (x + -0.5599987095) equal to 0.558890237 and -0.558890237.Subproblem 1
x + -0.5599987095 = 0.558890237 Simplifying x + -0.5599987095 = 0.558890237 Reorder the terms: -0.5599987095 + x = 0.558890237 Solving -0.5599987095 + x = 0.558890237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5599987095' to each side of the equation. -0.5599987095 + 0.5599987095 + x = 0.558890237 + 0.5599987095 Combine like terms: -0.5599987095 + 0.5599987095 = 0.0000000000 0.0000000000 + x = 0.558890237 + 0.5599987095 x = 0.558890237 + 0.5599987095 Combine like terms: 0.558890237 + 0.5599987095 = 1.1188889465 x = 1.1188889465 Simplifying x = 1.1188889465Subproblem 2
x + -0.5599987095 = -0.558890237 Simplifying x + -0.5599987095 = -0.558890237 Reorder the terms: -0.5599987095 + x = -0.558890237 Solving -0.5599987095 + x = -0.558890237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5599987095' to each side of the equation. -0.5599987095 + 0.5599987095 + x = -0.558890237 + 0.5599987095 Combine like terms: -0.5599987095 + 0.5599987095 = 0.0000000000 0.0000000000 + x = -0.558890237 + 0.5599987095 x = -0.558890237 + 0.5599987095 Combine like terms: -0.558890237 + 0.5599987095 = 0.0011084725 x = 0.0011084725 Simplifying x = 0.0011084725Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1188889465, 0.0011084725}
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