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Simplifying 26x2 + -48x + 5 = 0 Reorder the terms: 5 + -48x + 26x2 = 0 Solving 5 + -48x + 26x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 26 the coefficient of the squared term: Divide each side by '26'. 0.1923076923 + -1.846153846x + x2 = 0 Move the constant term to the right: Add '-0.1923076923' to each side of the equation. 0.1923076923 + -1.846153846x + -0.1923076923 + x2 = 0 + -0.1923076923 Reorder the terms: 0.1923076923 + -0.1923076923 + -1.846153846x + x2 = 0 + -0.1923076923 Combine like terms: 0.1923076923 + -0.1923076923 = 0.0000000000 0.0000000000 + -1.846153846x + x2 = 0 + -0.1923076923 -1.846153846x + x2 = 0 + -0.1923076923 Combine like terms: 0 + -0.1923076923 = -0.1923076923 -1.846153846x + x2 = -0.1923076923 The x term is -1.846153846x. Take half its coefficient (-0.923076923). Square it (0.8520710058) and add it to both sides. Add '0.8520710058' to each side of the equation. -1.846153846x + 0.8520710058 + x2 = -0.1923076923 + 0.8520710058 Reorder the terms: 0.8520710058 + -1.846153846x + x2 = -0.1923076923 + 0.8520710058 Combine like terms: -0.1923076923 + 0.8520710058 = 0.6597633135 0.8520710058 + -1.846153846x + x2 = 0.6597633135 Factor a perfect square on the left side: (x + -0.923076923)(x + -0.923076923) = 0.6597633135 Calculate the square root of the right side: 0.812258157 Break this problem into two subproblems by setting (x + -0.923076923) equal to 0.812258157 and -0.812258157.Subproblem 1
x + -0.923076923 = 0.812258157 Simplifying x + -0.923076923 = 0.812258157 Reorder the terms: -0.923076923 + x = 0.812258157 Solving -0.923076923 + x = 0.812258157 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.923076923' to each side of the equation. -0.923076923 + 0.923076923 + x = 0.812258157 + 0.923076923 Combine like terms: -0.923076923 + 0.923076923 = 0.000000000 0.000000000 + x = 0.812258157 + 0.923076923 x = 0.812258157 + 0.923076923 Combine like terms: 0.812258157 + 0.923076923 = 1.73533508 x = 1.73533508 Simplifying x = 1.73533508Subproblem 2
x + -0.923076923 = -0.812258157 Simplifying x + -0.923076923 = -0.812258157 Reorder the terms: -0.923076923 + x = -0.812258157 Solving -0.923076923 + x = -0.812258157 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.923076923' to each side of the equation. -0.923076923 + 0.923076923 + x = -0.812258157 + 0.923076923 Combine like terms: -0.923076923 + 0.923076923 = 0.000000000 0.000000000 + x = -0.812258157 + 0.923076923 x = -0.812258157 + 0.923076923 Combine like terms: -0.812258157 + 0.923076923 = 0.110818766 x = 0.110818766 Simplifying x = 0.110818766Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.73533508, 0.110818766}
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