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Simplifying 2.3x2 + -5x + -7.1 = 0 Reorder the terms: -7.1 + -5x + 2.3x2 = 0 Solving -7.1 + -5x + 2.3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.3 the coefficient of the squared term: Divide each side by '2.3'. -3.086956522 + -2.173913043x + x2 = 0 Move the constant term to the right: Add '3.086956522' to each side of the equation. -3.086956522 + -2.173913043x + 3.086956522 + x2 = 0 + 3.086956522 Reorder the terms: -3.086956522 + 3.086956522 + -2.173913043x + x2 = 0 + 3.086956522 Combine like terms: -3.086956522 + 3.086956522 = 0.000000000 0.000000000 + -2.173913043x + x2 = 0 + 3.086956522 -2.173913043x + x2 = 0 + 3.086956522 Combine like terms: 0 + 3.086956522 = 3.086956522 -2.173913043x + x2 = 3.086956522 The x term is -2.173913043x. Take half its coefficient (-1.086956522). Square it (1.181474481) and add it to both sides. Add '1.181474481' to each side of the equation. -2.173913043x + 1.181474481 + x2 = 3.086956522 + 1.181474481 Reorder the terms: 1.181474481 + -2.173913043x + x2 = 3.086956522 + 1.181474481 Combine like terms: 3.086956522 + 1.181474481 = 4.268431003 1.181474481 + -2.173913043x + x2 = 4.268431003 Factor a perfect square on the left side: (x + -1.086956522)(x + -1.086956522) = 4.268431003 Calculate the square root of the right side: 2.066018152 Break this problem into two subproblems by setting (x + -1.086956522) equal to 2.066018152 and -2.066018152.Subproblem 1
x + -1.086956522 = 2.066018152 Simplifying x + -1.086956522 = 2.066018152 Reorder the terms: -1.086956522 + x = 2.066018152 Solving -1.086956522 + x = 2.066018152 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.086956522' to each side of the equation. -1.086956522 + 1.086956522 + x = 2.066018152 + 1.086956522 Combine like terms: -1.086956522 + 1.086956522 = 0.000000000 0.000000000 + x = 2.066018152 + 1.086956522 x = 2.066018152 + 1.086956522 Combine like terms: 2.066018152 + 1.086956522 = 3.152974674 x = 3.152974674 Simplifying x = 3.152974674Subproblem 2
x + -1.086956522 = -2.066018152 Simplifying x + -1.086956522 = -2.066018152 Reorder the terms: -1.086956522 + x = -2.066018152 Solving -1.086956522 + x = -2.066018152 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.086956522' to each side of the equation. -1.086956522 + 1.086956522 + x = -2.066018152 + 1.086956522 Combine like terms: -1.086956522 + 1.086956522 = 0.000000000 0.000000000 + x = -2.066018152 + 1.086956522 x = -2.066018152 + 1.086956522 Combine like terms: -2.066018152 + 1.086956522 = -0.97906163 x = -0.97906163 Simplifying x = -0.97906163Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.152974674, -0.97906163}
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