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Simplifying 5.5x2 + -24x + 26 = 0 Reorder the terms: 26 + -24x + 5.5x2 = 0 Solving 26 + -24x + 5.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5.5 the coefficient of the squared term: Divide each side by '5.5'. 4.727272727 + -4.363636364x + x2 = 0 Move the constant term to the right: Add '-4.727272727' to each side of the equation. 4.727272727 + -4.363636364x + -4.727272727 + x2 = 0 + -4.727272727 Reorder the terms: 4.727272727 + -4.727272727 + -4.363636364x + x2 = 0 + -4.727272727 Combine like terms: 4.727272727 + -4.727272727 = 0.000000000 0.000000000 + -4.363636364x + x2 = 0 + -4.727272727 -4.363636364x + x2 = 0 + -4.727272727 Combine like terms: 0 + -4.727272727 = -4.727272727 -4.363636364x + x2 = -4.727272727 The x term is -4.363636364x. Take half its coefficient (-2.181818182). Square it (4.760330579) and add it to both sides. Add '4.760330579' to each side of the equation. -4.363636364x + 4.760330579 + x2 = -4.727272727 + 4.760330579 Reorder the terms: 4.760330579 + -4.363636364x + x2 = -4.727272727 + 4.760330579 Combine like terms: -4.727272727 + 4.760330579 = 0.033057852 4.760330579 + -4.363636364x + x2 = 0.033057852 Factor a perfect square on the left side: (x + -2.181818182)(x + -2.181818182) = 0.033057852 Calculate the square root of the right side: 0.181818184 Break this problem into two subproblems by setting (x + -2.181818182) equal to 0.181818184 and -0.181818184.Subproblem 1
x + -2.181818182 = 0.181818184 Simplifying x + -2.181818182 = 0.181818184 Reorder the terms: -2.181818182 + x = 0.181818184 Solving -2.181818182 + x = 0.181818184 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.181818182' to each side of the equation. -2.181818182 + 2.181818182 + x = 0.181818184 + 2.181818182 Combine like terms: -2.181818182 + 2.181818182 = 0.000000000 0.000000000 + x = 0.181818184 + 2.181818182 x = 0.181818184 + 2.181818182 Combine like terms: 0.181818184 + 2.181818182 = 2.363636366 x = 2.363636366 Simplifying x = 2.363636366Subproblem 2
x + -2.181818182 = -0.181818184 Simplifying x + -2.181818182 = -0.181818184 Reorder the terms: -2.181818182 + x = -0.181818184 Solving -2.181818182 + x = -0.181818184 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.181818182' to each side of the equation. -2.181818182 + 2.181818182 + x = -0.181818184 + 2.181818182 Combine like terms: -2.181818182 + 2.181818182 = 0.000000000 0.000000000 + x = -0.181818184 + 2.181818182 x = -0.181818184 + 2.181818182 Combine like terms: -0.181818184 + 2.181818182 = 1.999999998 x = 1.999999998 Simplifying x = 1.999999998Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.363636366, 1.999999998}
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