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Simplifying 23x2 + -264x + 109 = 0 Reorder the terms: 109 + -264x + 23x2 = 0 Solving 109 + -264x + 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'. 4.739130435 + -11.47826087x + x2 = 0 Move the constant term to the right: Add '-4.739130435' to each side of the equation. 4.739130435 + -11.47826087x + -4.739130435 + x2 = 0 + -4.739130435 Reorder the terms: 4.739130435 + -4.739130435 + -11.47826087x + x2 = 0 + -4.739130435 Combine like terms: 4.739130435 + -4.739130435 = 0.000000000 0.000000000 + -11.47826087x + x2 = 0 + -4.739130435 -11.47826087x + x2 = 0 + -4.739130435 Combine like terms: 0 + -4.739130435 = -4.739130435 -11.47826087x + x2 = -4.739130435 The x term is -11.47826087x. Take half its coefficient (-5.739130435). Square it (32.93761815) and add it to both sides. Add '32.93761815' to each side of the equation. -11.47826087x + 32.93761815 + x2 = -4.739130435 + 32.93761815 Reorder the terms: 32.93761815 + -11.47826087x + x2 = -4.739130435 + 32.93761815 Combine like terms: -4.739130435 + 32.93761815 = 28.198487715 32.93761815 + -11.47826087x + x2 = 28.198487715 Factor a perfect square on the left side: (x + -5.739130435)(x + -5.739130435) = 28.198487715 Calculate the square root of the right side: 5.310224827 Break this problem into two subproblems by setting (x + -5.739130435) equal to 5.310224827 and -5.310224827.Subproblem 1
x + -5.739130435 = 5.310224827 Simplifying x + -5.739130435 = 5.310224827 Reorder the terms: -5.739130435 + x = 5.310224827 Solving -5.739130435 + x = 5.310224827 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.739130435' to each side of the equation. -5.739130435 + 5.739130435 + x = 5.310224827 + 5.739130435 Combine like terms: -5.739130435 + 5.739130435 = 0.000000000 0.000000000 + x = 5.310224827 + 5.739130435 x = 5.310224827 + 5.739130435 Combine like terms: 5.310224827 + 5.739130435 = 11.049355262 x = 11.049355262 Simplifying x = 11.049355262Subproblem 2
x + -5.739130435 = -5.310224827 Simplifying x + -5.739130435 = -5.310224827 Reorder the terms: -5.739130435 + x = -5.310224827 Solving -5.739130435 + x = -5.310224827 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.739130435' to each side of the equation. -5.739130435 + 5.739130435 + x = -5.310224827 + 5.739130435 Combine like terms: -5.739130435 + 5.739130435 = 0.000000000 0.000000000 + x = -5.310224827 + 5.739130435 x = -5.310224827 + 5.739130435 Combine like terms: -5.310224827 + 5.739130435 = 0.428905608 x = 0.428905608 Simplifying x = 0.428905608Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.049355262, 0.428905608}
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