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Simplifying 1.4x2 + 3.3x + 0.8 = 0 Reorder the terms: 0.8 + 3.3x + 1.4x2 = 0 Solving 0.8 + 3.3x + 1.4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.4 the coefficient of the squared term: Divide each side by '1.4'. 0.5714285714 + 2.357142857x + x2 = 0 Move the constant term to the right: Add '-0.5714285714' to each side of the equation. 0.5714285714 + 2.357142857x + -0.5714285714 + x2 = 0 + -0.5714285714 Reorder the terms: 0.5714285714 + -0.5714285714 + 2.357142857x + x2 = 0 + -0.5714285714 Combine like terms: 0.5714285714 + -0.5714285714 = 0.0000000000 0.0000000000 + 2.357142857x + x2 = 0 + -0.5714285714 2.357142857x + x2 = 0 + -0.5714285714 Combine like terms: 0 + -0.5714285714 = -0.5714285714 2.357142857x + x2 = -0.5714285714 The x term is 2.357142857x. Take half its coefficient (1.178571429). Square it (1.389030613) and add it to both sides. Add '1.389030613' to each side of the equation. 2.357142857x + 1.389030613 + x2 = -0.5714285714 + 1.389030613 Reorder the terms: 1.389030613 + 2.357142857x + x2 = -0.5714285714 + 1.389030613 Combine like terms: -0.5714285714 + 1.389030613 = 0.8176020416 1.389030613 + 2.357142857x + x2 = 0.8176020416 Factor a perfect square on the left side: (x + 1.178571429)(x + 1.178571429) = 0.8176020416 Calculate the square root of the right side: 0.904213493 Break this problem into two subproblems by setting (x + 1.178571429) equal to 0.904213493 and -0.904213493.Subproblem 1
x + 1.178571429 = 0.904213493 Simplifying x + 1.178571429 = 0.904213493 Reorder the terms: 1.178571429 + x = 0.904213493 Solving 1.178571429 + x = 0.904213493 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.178571429' to each side of the equation. 1.178571429 + -1.178571429 + x = 0.904213493 + -1.178571429 Combine like terms: 1.178571429 + -1.178571429 = 0.000000000 0.000000000 + x = 0.904213493 + -1.178571429 x = 0.904213493 + -1.178571429 Combine like terms: 0.904213493 + -1.178571429 = -0.274357936 x = -0.274357936 Simplifying x = -0.274357936Subproblem 2
x + 1.178571429 = -0.904213493 Simplifying x + 1.178571429 = -0.904213493 Reorder the terms: 1.178571429 + x = -0.904213493 Solving 1.178571429 + x = -0.904213493 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.178571429' to each side of the equation. 1.178571429 + -1.178571429 + x = -0.904213493 + -1.178571429 Combine like terms: 1.178571429 + -1.178571429 = 0.000000000 0.000000000 + x = -0.904213493 + -1.178571429 x = -0.904213493 + -1.178571429 Combine like terms: -0.904213493 + -1.178571429 = -2.082784922 x = -2.082784922 Simplifying x = -2.082784922Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.274357936, -2.082784922}
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