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Simplifying -1.2x2 + -4x + 3.2 = 1.1 Reorder the terms: 3.2 + -4x + -1.2x2 = 1.1 Solving 3.2 + -4x + -1.2x2 = 1.1 Solving for variable 'x'. Reorder the terms: 3.2 + -1.1 + -4x + -1.2x2 = 1.1 + -1.1 Combine like terms: 3.2 + -1.1 = 2.1 2.1 + -4x + -1.2x2 = 1.1 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 2.1 + -4x + -1.2x2 = 0.0 Begin completing the square. Divide all terms by -1.2 the coefficient of the squared term: Divide each side by '-1.2'. -1.75 + 3.333333333x + x2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + 3.333333333x + 1.75 + x2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + 3.333333333x + x2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + 3.333333333x + x2 = 0 + 1.75 3.333333333x + x2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 3.333333333x + x2 = 1.75 The x term is 3.333333333x. Take half its coefficient (1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. 3.333333333x + 2.777777779 + x2 = 1.75 + 2.777777779 Reorder the terms: 2.777777779 + 3.333333333x + x2 = 1.75 + 2.777777779 Combine like terms: 1.75 + 2.777777779 = 4.527777779 2.777777779 + 3.333333333x + x2 = 4.527777779 Factor a perfect square on the left side: (x + 1.666666667)(x + 1.666666667) = 4.527777779 Calculate the square root of the right side: 2.127857556 Break this problem into two subproblems by setting (x + 1.666666667) equal to 2.127857556 and -2.127857556.Subproblem 1
x + 1.666666667 = 2.127857556 Simplifying x + 1.666666667 = 2.127857556 Reorder the terms: 1.666666667 + x = 2.127857556 Solving 1.666666667 + x = 2.127857556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = 2.127857556 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = 2.127857556 + -1.666666667 x = 2.127857556 + -1.666666667 Combine like terms: 2.127857556 + -1.666666667 = 0.461190889 x = 0.461190889 Simplifying x = 0.461190889Subproblem 2
x + 1.666666667 = -2.127857556 Simplifying x + 1.666666667 = -2.127857556 Reorder the terms: 1.666666667 + x = -2.127857556 Solving 1.666666667 + x = -2.127857556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = -2.127857556 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = -2.127857556 + -1.666666667 x = -2.127857556 + -1.666666667 Combine like terms: -2.127857556 + -1.666666667 = -3.794524223 x = -3.794524223 Simplifying x = -3.794524223Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.461190889, -3.794524223}
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