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Simplifying 20x2 + -47x + 11 = 0 Reorder the terms: 11 + -47x + 20x2 = 0 Solving 11 + -47x + 20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 0.55 + -2.35x + x2 = 0 Move the constant term to the right: Add '-0.55' to each side of the equation. 0.55 + -2.35x + -0.55 + x2 = 0 + -0.55 Reorder the terms: 0.55 + -0.55 + -2.35x + x2 = 0 + -0.55 Combine like terms: 0.55 + -0.55 = 0.00 0.00 + -2.35x + x2 = 0 + -0.55 -2.35x + x2 = 0 + -0.55 Combine like terms: 0 + -0.55 = -0.55 -2.35x + x2 = -0.55 The x term is -2.35x. Take half its coefficient (-1.175). Square it (1.380625) and add it to both sides. Add '1.380625' to each side of the equation. -2.35x + 1.380625 + x2 = -0.55 + 1.380625 Reorder the terms: 1.380625 + -2.35x + x2 = -0.55 + 1.380625 Combine like terms: -0.55 + 1.380625 = 0.830625 1.380625 + -2.35x + x2 = 0.830625 Factor a perfect square on the left side: (x + -1.175)(x + -1.175) = 0.830625 Calculate the square root of the right side: 0.911386307 Break this problem into two subproblems by setting (x + -1.175) equal to 0.911386307 and -0.911386307.Subproblem 1
x + -1.175 = 0.911386307 Simplifying x + -1.175 = 0.911386307 Reorder the terms: -1.175 + x = 0.911386307 Solving -1.175 + x = 0.911386307 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.175' to each side of the equation. -1.175 + 1.175 + x = 0.911386307 + 1.175 Combine like terms: -1.175 + 1.175 = 0.000 0.000 + x = 0.911386307 + 1.175 x = 0.911386307 + 1.175 Combine like terms: 0.911386307 + 1.175 = 2.086386307 x = 2.086386307 Simplifying x = 2.086386307Subproblem 2
x + -1.175 = -0.911386307 Simplifying x + -1.175 = -0.911386307 Reorder the terms: -1.175 + x = -0.911386307 Solving -1.175 + x = -0.911386307 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.175' to each side of the equation. -1.175 + 1.175 + x = -0.911386307 + 1.175 Combine like terms: -1.175 + 1.175 = 0.000 0.000 + x = -0.911386307 + 1.175 x = -0.911386307 + 1.175 Combine like terms: -0.911386307 + 1.175 = 0.263613693 x = 0.263613693 Simplifying x = 0.263613693Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.086386307, 0.263613693}
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