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Simplifying 2.1x2 + -6.6x + 4.9 = 0 Reorder the terms: 4.9 + -6.6x + 2.1x2 = 0 Solving 4.9 + -6.6x + 2.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.1 the coefficient of the squared term: Divide each side by '2.1'. 2.333333333 + -3.142857143x + x2 = 0 Move the constant term to the right: Add '-2.333333333' to each side of the equation. 2.333333333 + -3.142857143x + -2.333333333 + x2 = 0 + -2.333333333 Reorder the terms: 2.333333333 + -2.333333333 + -3.142857143x + x2 = 0 + -2.333333333 Combine like terms: 2.333333333 + -2.333333333 = 0.000000000 0.000000000 + -3.142857143x + x2 = 0 + -2.333333333 -3.142857143x + x2 = 0 + -2.333333333 Combine like terms: 0 + -2.333333333 = -2.333333333 -3.142857143x + x2 = -2.333333333 The x term is -3.142857143x. Take half its coefficient (-1.571428572). Square it (2.469387757) and add it to both sides. Add '2.469387757' to each side of the equation. -3.142857143x + 2.469387757 + x2 = -2.333333333 + 2.469387757 Reorder the terms: 2.469387757 + -3.142857143x + x2 = -2.333333333 + 2.469387757 Combine like terms: -2.333333333 + 2.469387757 = 0.136054424 2.469387757 + -3.142857143x + x2 = 0.136054424 Factor a perfect square on the left side: (x + -1.571428572)(x + -1.571428572) = 0.136054424 Calculate the square root of the right side: 0.36885556 Break this problem into two subproblems by setting (x + -1.571428572) equal to 0.36885556 and -0.36885556.Subproblem 1
x + -1.571428572 = 0.36885556 Simplifying x + -1.571428572 = 0.36885556 Reorder the terms: -1.571428572 + x = 0.36885556 Solving -1.571428572 + x = 0.36885556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.571428572' to each side of the equation. -1.571428572 + 1.571428572 + x = 0.36885556 + 1.571428572 Combine like terms: -1.571428572 + 1.571428572 = 0.000000000 0.000000000 + x = 0.36885556 + 1.571428572 x = 0.36885556 + 1.571428572 Combine like terms: 0.36885556 + 1.571428572 = 1.940284132 x = 1.940284132 Simplifying x = 1.940284132Subproblem 2
x + -1.571428572 = -0.36885556 Simplifying x + -1.571428572 = -0.36885556 Reorder the terms: -1.571428572 + x = -0.36885556 Solving -1.571428572 + x = -0.36885556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.571428572' to each side of the equation. -1.571428572 + 1.571428572 + x = -0.36885556 + 1.571428572 Combine like terms: -1.571428572 + 1.571428572 = 0.000000000 0.000000000 + x = -0.36885556 + 1.571428572 x = -0.36885556 + 1.571428572 Combine like terms: -0.36885556 + 1.571428572 = 1.202573012 x = 1.202573012 Simplifying x = 1.202573012Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.940284132, 1.202573012}
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