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Simplifying 23x2 + -5x + -42 = 0 Reorder the terms: -42 + -5x + 23x2 = 0 Solving -42 + -5x + 23x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 23 the coefficient of the squared term: Divide each side by '23'. -1.826086957 + -0.2173913043x + x2 = 0 Move the constant term to the right: Add '1.826086957' to each side of the equation. -1.826086957 + -0.2173913043x + 1.826086957 + x2 = 0 + 1.826086957 Reorder the terms: -1.826086957 + 1.826086957 + -0.2173913043x + x2 = 0 + 1.826086957 Combine like terms: -1.826086957 + 1.826086957 = 0.000000000 0.000000000 + -0.2173913043x + x2 = 0 + 1.826086957 -0.2173913043x + x2 = 0 + 1.826086957 Combine like terms: 0 + 1.826086957 = 1.826086957 -0.2173913043x + x2 = 1.826086957 The x term is -0.2173913043x. Take half its coefficient (-0.1086956522). Square it (0.01181474481) and add it to both sides. Add '0.01181474481' to each side of the equation. -0.2173913043x + 0.01181474481 + x2 = 1.826086957 + 0.01181474481 Reorder the terms: 0.01181474481 + -0.2173913043x + x2 = 1.826086957 + 0.01181474481 Combine like terms: 1.826086957 + 0.01181474481 = 1.83790170181 0.01181474481 + -0.2173913043x + x2 = 1.83790170181 Factor a perfect square on the left side: (x + -0.1086956522)(x + -0.1086956522) = 1.83790170181 Calculate the square root of the right side: 1.355692333 Break this problem into two subproblems by setting (x + -0.1086956522) equal to 1.355692333 and -1.355692333.Subproblem 1
x + -0.1086956522 = 1.355692333 Simplifying x + -0.1086956522 = 1.355692333 Reorder the terms: -0.1086956522 + x = 1.355692333 Solving -0.1086956522 + x = 1.355692333 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1086956522' to each side of the equation. -0.1086956522 + 0.1086956522 + x = 1.355692333 + 0.1086956522 Combine like terms: -0.1086956522 + 0.1086956522 = 0.0000000000 0.0000000000 + x = 1.355692333 + 0.1086956522 x = 1.355692333 + 0.1086956522 Combine like terms: 1.355692333 + 0.1086956522 = 1.4643879852 x = 1.4643879852 Simplifying x = 1.4643879852Subproblem 2
x + -0.1086956522 = -1.355692333 Simplifying x + -0.1086956522 = -1.355692333 Reorder the terms: -0.1086956522 + x = -1.355692333 Solving -0.1086956522 + x = -1.355692333 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1086956522' to each side of the equation. -0.1086956522 + 0.1086956522 + x = -1.355692333 + 0.1086956522 Combine like terms: -0.1086956522 + 0.1086956522 = 0.0000000000 0.0000000000 + x = -1.355692333 + 0.1086956522 x = -1.355692333 + 0.1086956522 Combine like terms: -1.355692333 + 0.1086956522 = -1.2469966808 x = -1.2469966808 Simplifying x = -1.2469966808Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4643879852, -1.2469966808}
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