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Simplifying 23x2 + 32x + -20 = 0 Reorder the terms: -20 + 32x + 23x2 = 0 Solving -20 + 32x + 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'. -0.8695652174 + 1.391304348x + x2 = 0 Move the constant term to the right: Add '0.8695652174' to each side of the equation. -0.8695652174 + 1.391304348x + 0.8695652174 + x2 = 0 + 0.8695652174 Reorder the terms: -0.8695652174 + 0.8695652174 + 1.391304348x + x2 = 0 + 0.8695652174 Combine like terms: -0.8695652174 + 0.8695652174 = 0.0000000000 0.0000000000 + 1.391304348x + x2 = 0 + 0.8695652174 1.391304348x + x2 = 0 + 0.8695652174 Combine like terms: 0 + 0.8695652174 = 0.8695652174 1.391304348x + x2 = 0.8695652174 The x term is 1.391304348x. Take half its coefficient (0.695652174). Square it (0.4839319472) and add it to both sides. Add '0.4839319472' to each side of the equation. 1.391304348x + 0.4839319472 + x2 = 0.8695652174 + 0.4839319472 Reorder the terms: 0.4839319472 + 1.391304348x + x2 = 0.8695652174 + 0.4839319472 Combine like terms: 0.8695652174 + 0.4839319472 = 1.3534971646 0.4839319472 + 1.391304348x + x2 = 1.3534971646 Factor a perfect square on the left side: (x + 0.695652174)(x + 0.695652174) = 1.3534971646 Calculate the square root of the right side: 1.163398971 Break this problem into two subproblems by setting (x + 0.695652174) equal to 1.163398971 and -1.163398971.Subproblem 1
x + 0.695652174 = 1.163398971 Simplifying x + 0.695652174 = 1.163398971 Reorder the terms: 0.695652174 + x = 1.163398971 Solving 0.695652174 + x = 1.163398971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.695652174' to each side of the equation. 0.695652174 + -0.695652174 + x = 1.163398971 + -0.695652174 Combine like terms: 0.695652174 + -0.695652174 = 0.000000000 0.000000000 + x = 1.163398971 + -0.695652174 x = 1.163398971 + -0.695652174 Combine like terms: 1.163398971 + -0.695652174 = 0.467746797 x = 0.467746797 Simplifying x = 0.467746797Subproblem 2
x + 0.695652174 = -1.163398971 Simplifying x + 0.695652174 = -1.163398971 Reorder the terms: 0.695652174 + x = -1.163398971 Solving 0.695652174 + x = -1.163398971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.695652174' to each side of the equation. 0.695652174 + -0.695652174 + x = -1.163398971 + -0.695652174 Combine like terms: 0.695652174 + -0.695652174 = 0.000000000 0.000000000 + x = -1.163398971 + -0.695652174 x = -1.163398971 + -0.695652174 Combine like terms: -1.163398971 + -0.695652174 = -1.859051145 x = -1.859051145 Simplifying x = -1.859051145Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.467746797, -1.859051145}
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