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Simplifying -1.4375x2 + -4.375x + -0.9375 = 0 Reorder the terms: -0.9375 + -4.375x + -1.4375x2 = 0 Solving -0.9375 + -4.375x + -1.4375x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1.4375 the coefficient of the squared term: Divide each side by '-1.4375'. 0.652173913 + 3.043478261x + x2 = 0 Move the constant term to the right: Add '-0.652173913' to each side of the equation. 0.652173913 + 3.043478261x + -0.652173913 + x2 = 0 + -0.652173913 Reorder the terms: 0.652173913 + -0.652173913 + 3.043478261x + x2 = 0 + -0.652173913 Combine like terms: 0.652173913 + -0.652173913 = 0.000000000 0.000000000 + 3.043478261x + x2 = 0 + -0.652173913 3.043478261x + x2 = 0 + -0.652173913 Combine like terms: 0 + -0.652173913 = -0.652173913 3.043478261x + x2 = -0.652173913 The x term is 3.043478261x. Take half its coefficient (1.521739131). Square it (2.315689983) and add it to both sides. Add '2.315689983' to each side of the equation. 3.043478261x + 2.315689983 + x2 = -0.652173913 + 2.315689983 Reorder the terms: 2.315689983 + 3.043478261x + x2 = -0.652173913 + 2.315689983 Combine like terms: -0.652173913 + 2.315689983 = 1.66351607 2.315689983 + 3.043478261x + x2 = 1.66351607 Factor a perfect square on the left side: (x + 1.521739131)(x + 1.521739131) = 1.66351607 Calculate the square root of the right side: 1.289773651 Break this problem into two subproblems by setting (x + 1.521739131) equal to 1.289773651 and -1.289773651.Subproblem 1
x + 1.521739131 = 1.289773651 Simplifying x + 1.521739131 = 1.289773651 Reorder the terms: 1.521739131 + x = 1.289773651 Solving 1.521739131 + x = 1.289773651 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.521739131' to each side of the equation. 1.521739131 + -1.521739131 + x = 1.289773651 + -1.521739131 Combine like terms: 1.521739131 + -1.521739131 = 0.000000000 0.000000000 + x = 1.289773651 + -1.521739131 x = 1.289773651 + -1.521739131 Combine like terms: 1.289773651 + -1.521739131 = -0.23196548 x = -0.23196548 Simplifying x = -0.23196548Subproblem 2
x + 1.521739131 = -1.289773651 Simplifying x + 1.521739131 = -1.289773651 Reorder the terms: 1.521739131 + x = -1.289773651 Solving 1.521739131 + x = -1.289773651 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.521739131' to each side of the equation. 1.521739131 + -1.521739131 + x = -1.289773651 + -1.521739131 Combine like terms: 1.521739131 + -1.521739131 = 0.000000000 0.000000000 + x = -1.289773651 + -1.521739131 x = -1.289773651 + -1.521739131 Combine like terms: -1.289773651 + -1.521739131 = -2.811512782 x = -2.811512782 Simplifying x = -2.811512782Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.23196548, -2.811512782}
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