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Simplifying 26x2 + -160x + 211 = 0 Reorder the terms: 211 + -160x + 26x2 = 0 Solving 211 + -160x + 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'. 8.115384615 + -6.153846154x + x2 = 0 Move the constant term to the right: Add '-8.115384615' to each side of the equation. 8.115384615 + -6.153846154x + -8.115384615 + x2 = 0 + -8.115384615 Reorder the terms: 8.115384615 + -8.115384615 + -6.153846154x + x2 = 0 + -8.115384615 Combine like terms: 8.115384615 + -8.115384615 = 0.000000000 0.000000000 + -6.153846154x + x2 = 0 + -8.115384615 -6.153846154x + x2 = 0 + -8.115384615 Combine like terms: 0 + -8.115384615 = -8.115384615 -6.153846154x + x2 = -8.115384615 The x term is -6.153846154x. Take half its coefficient (-3.076923077). Square it (9.467455622) and add it to both sides. Add '9.467455622' to each side of the equation. -6.153846154x + 9.467455622 + x2 = -8.115384615 + 9.467455622 Reorder the terms: 9.467455622 + -6.153846154x + x2 = -8.115384615 + 9.467455622 Combine like terms: -8.115384615 + 9.467455622 = 1.352071007 9.467455622 + -6.153846154x + x2 = 1.352071007 Factor a perfect square on the left side: (x + -3.076923077)(x + -3.076923077) = 1.352071007 Calculate the square root of the right side: 1.162785882 Break this problem into two subproblems by setting (x + -3.076923077) equal to 1.162785882 and -1.162785882.Subproblem 1
x + -3.076923077 = 1.162785882 Simplifying x + -3.076923077 = 1.162785882 Reorder the terms: -3.076923077 + x = 1.162785882 Solving -3.076923077 + x = 1.162785882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.076923077' to each side of the equation. -3.076923077 + 3.076923077 + x = 1.162785882 + 3.076923077 Combine like terms: -3.076923077 + 3.076923077 = 0.000000000 0.000000000 + x = 1.162785882 + 3.076923077 x = 1.162785882 + 3.076923077 Combine like terms: 1.162785882 + 3.076923077 = 4.239708959 x = 4.239708959 Simplifying x = 4.239708959Subproblem 2
x + -3.076923077 = -1.162785882 Simplifying x + -3.076923077 = -1.162785882 Reorder the terms: -3.076923077 + x = -1.162785882 Solving -3.076923077 + x = -1.162785882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.076923077' to each side of the equation. -3.076923077 + 3.076923077 + x = -1.162785882 + 3.076923077 Combine like terms: -3.076923077 + 3.076923077 = 0.000000000 0.000000000 + x = -1.162785882 + 3.076923077 x = -1.162785882 + 3.076923077 Combine like terms: -1.162785882 + 3.076923077 = 1.914137195 x = 1.914137195 Simplifying x = 1.914137195Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.239708959, 1.914137195}
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