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Simplifying -0.9x2 + -1.4x + 3 = 0 Reorder the terms: 3 + -1.4x + -0.9x2 = 0 Solving 3 + -1.4x + -0.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.9 the coefficient of the squared term: Divide each side by '-0.9'. -3.333333333 + 1.555555556x + x2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + 1.555555556x + 3.333333333 + x2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + 1.555555556x + x2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + 1.555555556x + x2 = 0 + 3.333333333 1.555555556x + x2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 1.555555556x + x2 = 3.333333333 The x term is 1.555555556x. Take half its coefficient (0.777777778). Square it (0.6049382720) and add it to both sides. Add '0.6049382720' to each side of the equation. 1.555555556x + 0.6049382720 + x2 = 3.333333333 + 0.6049382720 Reorder the terms: 0.6049382720 + 1.555555556x + x2 = 3.333333333 + 0.6049382720 Combine like terms: 3.333333333 + 0.6049382720 = 3.938271605 0.6049382720 + 1.555555556x + x2 = 3.938271605 Factor a perfect square on the left side: (x + 0.777777778)(x + 0.777777778) = 3.938271605 Calculate the square root of the right side: 1.9845079 Break this problem into two subproblems by setting (x + 0.777777778) equal to 1.9845079 and -1.9845079.Subproblem 1
x + 0.777777778 = 1.9845079 Simplifying x + 0.777777778 = 1.9845079 Reorder the terms: 0.777777778 + x = 1.9845079 Solving 0.777777778 + x = 1.9845079 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.777777778' to each side of the equation. 0.777777778 + -0.777777778 + x = 1.9845079 + -0.777777778 Combine like terms: 0.777777778 + -0.777777778 = 0.000000000 0.000000000 + x = 1.9845079 + -0.777777778 x = 1.9845079 + -0.777777778 Combine like terms: 1.9845079 + -0.777777778 = 1.206730122 x = 1.206730122 Simplifying x = 1.206730122Subproblem 2
x + 0.777777778 = -1.9845079 Simplifying x + 0.777777778 = -1.9845079 Reorder the terms: 0.777777778 + x = -1.9845079 Solving 0.777777778 + x = -1.9845079 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.777777778' to each side of the equation. 0.777777778 + -0.777777778 + x = -1.9845079 + -0.777777778 Combine like terms: 0.777777778 + -0.777777778 = 0.000000000 0.000000000 + x = -1.9845079 + -0.777777778 x = -1.9845079 + -0.777777778 Combine like terms: -1.9845079 + -0.777777778 = -2.762285678 x = -2.762285678 Simplifying x = -2.762285678Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.206730122, -2.762285678}
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