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Simplifying 21x2 + -61x + 6 = 0 Reorder the terms: 6 + -61x + 21x2 = 0 Solving 6 + -61x + 21x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. 0.2857142857 + -2.904761905x + x2 = 0 Move the constant term to the right: Add '-0.2857142857' to each side of the equation. 0.2857142857 + -2.904761905x + -0.2857142857 + x2 = 0 + -0.2857142857 Reorder the terms: 0.2857142857 + -0.2857142857 + -2.904761905x + x2 = 0 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + -2.904761905x + x2 = 0 + -0.2857142857 -2.904761905x + x2 = 0 + -0.2857142857 Combine like terms: 0 + -0.2857142857 = -0.2857142857 -2.904761905x + x2 = -0.2857142857 The x term is -2.904761905x. Take half its coefficient (-1.452380953). Square it (2.109410433) and add it to both sides. Add '2.109410433' to each side of the equation. -2.904761905x + 2.109410433 + x2 = -0.2857142857 + 2.109410433 Reorder the terms: 2.109410433 + -2.904761905x + x2 = -0.2857142857 + 2.109410433 Combine like terms: -0.2857142857 + 2.109410433 = 1.8236961473 2.109410433 + -2.904761905x + x2 = 1.8236961473 Factor a perfect square on the left side: (x + -1.452380953)(x + -1.452380953) = 1.8236961473 Calculate the square root of the right side: 1.350442945 Break this problem into two subproblems by setting (x + -1.452380953) equal to 1.350442945 and -1.350442945.Subproblem 1
x + -1.452380953 = 1.350442945 Simplifying x + -1.452380953 = 1.350442945 Reorder the terms: -1.452380953 + x = 1.350442945 Solving -1.452380953 + x = 1.350442945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.452380953' to each side of the equation. -1.452380953 + 1.452380953 + x = 1.350442945 + 1.452380953 Combine like terms: -1.452380953 + 1.452380953 = 0.000000000 0.000000000 + x = 1.350442945 + 1.452380953 x = 1.350442945 + 1.452380953 Combine like terms: 1.350442945 + 1.452380953 = 2.802823898 x = 2.802823898 Simplifying x = 2.802823898Subproblem 2
x + -1.452380953 = -1.350442945 Simplifying x + -1.452380953 = -1.350442945 Reorder the terms: -1.452380953 + x = -1.350442945 Solving -1.452380953 + x = -1.350442945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.452380953' to each side of the equation. -1.452380953 + 1.452380953 + x = -1.350442945 + 1.452380953 Combine like terms: -1.452380953 + 1.452380953 = 0.000000000 0.000000000 + x = -1.350442945 + 1.452380953 x = -1.350442945 + 1.452380953 Combine like terms: -1.350442945 + 1.452380953 = 0.101938008 x = 0.101938008 Simplifying x = 0.101938008Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.802823898, 0.101938008}
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