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Simplifying 55x2 + -233x + 126 = 110 Reorder the terms: 126 + -233x + 55x2 = 110 Solving 126 + -233x + 55x2 = 110 Solving for variable 'x'. Reorder the terms: 126 + -110 + -233x + 55x2 = 110 + -110 Combine like terms: 126 + -110 = 16 16 + -233x + 55x2 = 110 + -110 Combine like terms: 110 + -110 = 0 16 + -233x + 55x2 = 0 Begin completing the square. Divide all terms by 55 the coefficient of the squared term: Divide each side by '55'. 0.2909090909 + -4.236363636x + x2 = 0 Move the constant term to the right: Add '-0.2909090909' to each side of the equation. 0.2909090909 + -4.236363636x + -0.2909090909 + x2 = 0 + -0.2909090909 Reorder the terms: 0.2909090909 + -0.2909090909 + -4.236363636x + x2 = 0 + -0.2909090909 Combine like terms: 0.2909090909 + -0.2909090909 = 0.0000000000 0.0000000000 + -4.236363636x + x2 = 0 + -0.2909090909 -4.236363636x + x2 = 0 + -0.2909090909 Combine like terms: 0 + -0.2909090909 = -0.2909090909 -4.236363636x + x2 = -0.2909090909 The x term is -4.236363636x. Take half its coefficient (-2.118181818). Square it (4.486694214) and add it to both sides. Add '4.486694214' to each side of the equation. -4.236363636x + 4.486694214 + x2 = -0.2909090909 + 4.486694214 Reorder the terms: 4.486694214 + -4.236363636x + x2 = -0.2909090909 + 4.486694214 Combine like terms: -0.2909090909 + 4.486694214 = 4.1957851231 4.486694214 + -4.236363636x + x2 = 4.1957851231 Factor a perfect square on the left side: (x + -2.118181818)(x + -2.118181818) = 4.1957851231 Calculate the square root of the right side: 2.04836157 Break this problem into two subproblems by setting (x + -2.118181818) equal to 2.04836157 and -2.04836157.Subproblem 1
x + -2.118181818 = 2.04836157 Simplifying x + -2.118181818 = 2.04836157 Reorder the terms: -2.118181818 + x = 2.04836157 Solving -2.118181818 + x = 2.04836157 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.118181818' to each side of the equation. -2.118181818 + 2.118181818 + x = 2.04836157 + 2.118181818 Combine like terms: -2.118181818 + 2.118181818 = 0.000000000 0.000000000 + x = 2.04836157 + 2.118181818 x = 2.04836157 + 2.118181818 Combine like terms: 2.04836157 + 2.118181818 = 4.166543388 x = 4.166543388 Simplifying x = 4.166543388Subproblem 2
x + -2.118181818 = -2.04836157 Simplifying x + -2.118181818 = -2.04836157 Reorder the terms: -2.118181818 + x = -2.04836157 Solving -2.118181818 + x = -2.04836157 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.118181818' to each side of the equation. -2.118181818 + 2.118181818 + x = -2.04836157 + 2.118181818 Combine like terms: -2.118181818 + 2.118181818 = 0.000000000 0.000000000 + x = -2.04836157 + 2.118181818 x = -2.04836157 + 2.118181818 Combine like terms: -2.04836157 + 2.118181818 = 0.069820248 x = 0.069820248 Simplifying x = 0.069820248Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.166543388, 0.069820248}
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