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Simplifying -3.3X2 + -4.6X + -1.3 = 0 Reorder the terms: -1.3 + -4.6X + -3.3X2 = 0 Solving -1.3 + -4.6X + -3.3X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by -3.3 the coefficient of the squared term: Divide each side by '-3.3'. 0.3939393939 + 1.393939394X + X2 = 0 Move the constant term to the right: Add '-0.3939393939' to each side of the equation. 0.3939393939 + 1.393939394X + -0.3939393939 + X2 = 0 + -0.3939393939 Reorder the terms: 0.3939393939 + -0.3939393939 + 1.393939394X + X2 = 0 + -0.3939393939 Combine like terms: 0.3939393939 + -0.3939393939 = 0.0000000000 0.0000000000 + 1.393939394X + X2 = 0 + -0.3939393939 1.393939394X + X2 = 0 + -0.3939393939 Combine like terms: 0 + -0.3939393939 = -0.3939393939 1.393939394X + X2 = -0.3939393939 The X term is 1.393939394X. Take half its coefficient (0.696969697). Square it (0.4857667585) and add it to both sides. Add '0.4857667585' to each side of the equation. 1.393939394X + 0.4857667585 + X2 = -0.3939393939 + 0.4857667585 Reorder the terms: 0.4857667585 + 1.393939394X + X2 = -0.3939393939 + 0.4857667585 Combine like terms: -0.3939393939 + 0.4857667585 = 0.0918273646 0.4857667585 + 1.393939394X + X2 = 0.0918273646 Factor a perfect square on the left side: (X + 0.696969697)(X + 0.696969697) = 0.0918273646 Calculate the square root of the right side: 0.303030303 Break this problem into two subproblems by setting (X + 0.696969697) equal to 0.303030303 and -0.303030303.Subproblem 1
X + 0.696969697 = 0.303030303 Simplifying X + 0.696969697 = 0.303030303 Reorder the terms: 0.696969697 + X = 0.303030303 Solving 0.696969697 + X = 0.303030303 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.696969697' to each side of the equation. 0.696969697 + -0.696969697 + X = 0.303030303 + -0.696969697 Combine like terms: 0.696969697 + -0.696969697 = 0.000000000 0.000000000 + X = 0.303030303 + -0.696969697 X = 0.303030303 + -0.696969697 Combine like terms: 0.303030303 + -0.696969697 = -0.393939394 X = -0.393939394 Simplifying X = -0.393939394Subproblem 2
X + 0.696969697 = -0.303030303 Simplifying X + 0.696969697 = -0.303030303 Reorder the terms: 0.696969697 + X = -0.303030303 Solving 0.696969697 + X = -0.303030303 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.696969697' to each side of the equation. 0.696969697 + -0.696969697 + X = -0.303030303 + -0.696969697 Combine like terms: 0.696969697 + -0.696969697 = 0.000000000 0.000000000 + X = -0.303030303 + -0.696969697 X = -0.303030303 + -0.696969697 Combine like terms: -0.303030303 + -0.696969697 = -1 X = -1 Simplifying X = -1Solution
The solution to the problem is based on the solutions from the subproblems. X = {-0.393939394, -1}
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