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Simplifying 4.9x2 + -21x + 19 = 0 Reorder the terms: 19 + -21x + 4.9x2 = 0 Solving 19 + -21x + 4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. 3.87755102 + -4.285714286x + x2 = 0 Move the constant term to the right: Add '-3.87755102' to each side of the equation. 3.87755102 + -4.285714286x + -3.87755102 + x2 = 0 + -3.87755102 Reorder the terms: 3.87755102 + -3.87755102 + -4.285714286x + x2 = 0 + -3.87755102 Combine like terms: 3.87755102 + -3.87755102 = 0.00000000 0.00000000 + -4.285714286x + x2 = 0 + -3.87755102 -4.285714286x + x2 = 0 + -3.87755102 Combine like terms: 0 + -3.87755102 = -3.87755102 -4.285714286x + x2 = -3.87755102 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 = -3.87755102 + 4.591836735 Reorder the terms: 4.591836735 + -4.285714286x + x2 = -3.87755102 + 4.591836735 Combine like terms: -3.87755102 + 4.591836735 = 0.714285715 4.591836735 + -4.285714286x + x2 = 0.714285715 Factor a perfect square on the left side: (x + -2.142857143)(x + -2.142857143) = 0.714285715 Calculate the square root of the right side: 0.845154255 Break this problem into two subproblems by setting (x + -2.142857143) equal to 0.845154255 and -0.845154255.Subproblem 1
x + -2.142857143 = 0.845154255 Simplifying x + -2.142857143 = 0.845154255 Reorder the terms: -2.142857143 + x = 0.845154255 Solving -2.142857143 + x = 0.845154255 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 = 0.845154255 + 2.142857143 Combine like terms: -2.142857143 + 2.142857143 = 0.000000000 0.000000000 + x = 0.845154255 + 2.142857143 x = 0.845154255 + 2.142857143 Combine like terms: 0.845154255 + 2.142857143 = 2.988011398 x = 2.988011398 Simplifying x = 2.988011398Subproblem 2
x + -2.142857143 = -0.845154255 Simplifying x + -2.142857143 = -0.845154255 Reorder the terms: -2.142857143 + x = -0.845154255 Solving -2.142857143 + x = -0.845154255 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 = -0.845154255 + 2.142857143 Combine like terms: -2.142857143 + 2.142857143 = 0.000000000 0.000000000 + x = -0.845154255 + 2.142857143 x = -0.845154255 + 2.142857143 Combine like terms: -0.845154255 + 2.142857143 = 1.297702888 x = 1.297702888 Simplifying x = 1.297702888Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.988011398, 1.297702888}
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