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Simplifying 23x2 + -24x + 2 = 0 Reorder the terms: 2 + -24x + 23x2 = 0 Solving 2 + -24x + 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'. 0.08695652174 + -1.043478261x + x2 = 0 Move the constant term to the right: Add '-0.08695652174' to each side of the equation. 0.08695652174 + -1.043478261x + -0.08695652174 + x2 = 0 + -0.08695652174 Reorder the terms: 0.08695652174 + -0.08695652174 + -1.043478261x + x2 = 0 + -0.08695652174 Combine like terms: 0.08695652174 + -0.08695652174 = 0.00000000000 0.00000000000 + -1.043478261x + x2 = 0 + -0.08695652174 -1.043478261x + x2 = 0 + -0.08695652174 Combine like terms: 0 + -0.08695652174 = -0.08695652174 -1.043478261x + x2 = -0.08695652174 The x term is -1.043478261x. Take half its coefficient (-0.5217391305). Square it (0.2722117203) and add it to both sides. Add '0.2722117203' to each side of the equation. -1.043478261x + 0.2722117203 + x2 = -0.08695652174 + 0.2722117203 Reorder the terms: 0.2722117203 + -1.043478261x + x2 = -0.08695652174 + 0.2722117203 Combine like terms: -0.08695652174 + 0.2722117203 = 0.18525519856 0.2722117203 + -1.043478261x + x2 = 0.18525519856 Factor a perfect square on the left side: (x + -0.5217391305)(x + -0.5217391305) = 0.18525519856 Calculate the square root of the right side: 0.430412823 Break this problem into two subproblems by setting (x + -0.5217391305) equal to 0.430412823 and -0.430412823.Subproblem 1
x + -0.5217391305 = 0.430412823 Simplifying x + -0.5217391305 = 0.430412823 Reorder the terms: -0.5217391305 + x = 0.430412823 Solving -0.5217391305 + x = 0.430412823 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5217391305' to each side of the equation. -0.5217391305 + 0.5217391305 + x = 0.430412823 + 0.5217391305 Combine like terms: -0.5217391305 + 0.5217391305 = 0.0000000000 0.0000000000 + x = 0.430412823 + 0.5217391305 x = 0.430412823 + 0.5217391305 Combine like terms: 0.430412823 + 0.5217391305 = 0.9521519535 x = 0.9521519535 Simplifying x = 0.9521519535Subproblem 2
x + -0.5217391305 = -0.430412823 Simplifying x + -0.5217391305 = -0.430412823 Reorder the terms: -0.5217391305 + x = -0.430412823 Solving -0.5217391305 + x = -0.430412823 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5217391305' to each side of the equation. -0.5217391305 + 0.5217391305 + x = -0.430412823 + 0.5217391305 Combine like terms: -0.5217391305 + 0.5217391305 = 0.0000000000 0.0000000000 + x = -0.430412823 + 0.5217391305 x = -0.430412823 + 0.5217391305 Combine like terms: -0.430412823 + 0.5217391305 = 0.0913263075 x = 0.0913263075 Simplifying x = 0.0913263075Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9521519535, 0.0913263075}
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