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Simplifying 20.8 = 21x + -4.9x2 Solving 20.8 = 21x + -4.9x2 Solving for variable 'x'. Reorder the terms: 20.8 + -21x + 4.9x2 = 21x + -21x + -4.9x2 + 4.9x2 Combine like terms: 21x + -21x = 0 20.8 + -21x + 4.9x2 = 0 + -4.9x2 + 4.9x2 20.8 + -21x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 20.8 + -21x + 4.9x2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. 4.244897959 + -4.285714286x + x2 = 0 Move the constant term to the right: Add '-4.244897959' to each side of the equation. 4.244897959 + -4.285714286x + -4.244897959 + x2 = 0 + -4.244897959 Reorder the terms: 4.244897959 + -4.244897959 + -4.285714286x + x2 = 0 + -4.244897959 Combine like terms: 4.244897959 + -4.244897959 = 0.000000000 0.000000000 + -4.285714286x + x2 = 0 + -4.244897959 -4.285714286x + x2 = 0 + -4.244897959 Combine like terms: 0 + -4.244897959 = -4.244897959 -4.285714286x + x2 = -4.244897959 The x term is -4.285714286x. Take half its coefficient (-2.142857143). Square it (4.591836735) and add it to both sides. Add '4.591836735' to each side of the equation. -4.285714286x + 4.591836735 + x2 = -4.244897959 + 4.591836735 Reorder the terms: 4.591836735 + -4.285714286x + x2 = -4.244897959 + 4.591836735 Combine like terms: -4.244897959 + 4.591836735 = 0.346938776 4.591836735 + -4.285714286x + x2 = 0.346938776 Factor a perfect square on the left side: (x + -2.142857143)(x + -2.142857143) = 0.346938776 Calculate the square root of the right side: 0.58901509 Break this problem into two subproblems by setting (x + -2.142857143) equal to 0.58901509 and -0.58901509.Subproblem 1
x + -2.142857143 = 0.58901509 Simplifying x + -2.142857143 = 0.58901509 Reorder the terms: -2.142857143 + x = 0.58901509 Solving -2.142857143 + x = 0.58901509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.142857143' to each side of the equation. -2.142857143 + 2.142857143 + x = 0.58901509 + 2.142857143 Combine like terms: -2.142857143 + 2.142857143 = 0.000000000 0.000000000 + x = 0.58901509 + 2.142857143 x = 0.58901509 + 2.142857143 Combine like terms: 0.58901509 + 2.142857143 = 2.731872233 x = 2.731872233 Simplifying x = 2.731872233Subproblem 2
x + -2.142857143 = -0.58901509 Simplifying x + -2.142857143 = -0.58901509 Reorder the terms: -2.142857143 + x = -0.58901509 Solving -2.142857143 + x = -0.58901509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.142857143' to each side of the equation. -2.142857143 + 2.142857143 + x = -0.58901509 + 2.142857143 Combine like terms: -2.142857143 + 2.142857143 = 0.000000000 0.000000000 + x = -0.58901509 + 2.142857143 x = -0.58901509 + 2.142857143 Combine like terms: -0.58901509 + 2.142857143 = 1.553842053 x = 1.553842053 Simplifying x = 1.553842053Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.731872233, 1.553842053}
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