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Simplifying (26x2 + -310x + 910) = 0 Reorder the terms: (910 + -310x + 26x2) = 0 Remove parenthesis around (910 + -310x + 26x2) 910 + -310x + 26x2 = 0 Solving 910 + -310x + 26x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(455 + -155x + 13x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(455 + -155x + 13x2)' equal to zero and attempt to solve: Simplifying 455 + -155x + 13x2 = 0 Solving 455 + -155x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 35 + -11.92307692x + x2 = 0 Move the constant term to the right: Add '-35' to each side of the equation. 35 + -11.92307692x + -35 + x2 = 0 + -35 Reorder the terms: 35 + -35 + -11.92307692x + x2 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + -11.92307692x + x2 = 0 + -35 -11.92307692x + x2 = 0 + -35 Combine like terms: 0 + -35 = -35 -11.92307692x + x2 = -35 The x term is -11.92307692x. Take half its coefficient (-5.96153846). Square it (35.53994081) and add it to both sides. Add '35.53994081' to each side of the equation. -11.92307692x + 35.53994081 + x2 = -35 + 35.53994081 Reorder the terms: 35.53994081 + -11.92307692x + x2 = -35 + 35.53994081 Combine like terms: -35 + 35.53994081 = 0.53994081 35.53994081 + -11.92307692x + x2 = 0.53994081 Factor a perfect square on the left side: (x + -5.96153846)(x + -5.96153846) = 0.53994081 Calculate the square root of the right side: 0.734806648 Break this problem into two subproblems by setting (x + -5.96153846) equal to 0.734806648 and -0.734806648.Subproblem 1
x + -5.96153846 = 0.734806648 Simplifying x + -5.96153846 = 0.734806648 Reorder the terms: -5.96153846 + x = 0.734806648 Solving -5.96153846 + x = 0.734806648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.96153846' to each side of the equation. -5.96153846 + 5.96153846 + x = 0.734806648 + 5.96153846 Combine like terms: -5.96153846 + 5.96153846 = 0.00000000 0.00000000 + x = 0.734806648 + 5.96153846 x = 0.734806648 + 5.96153846 Combine like terms: 0.734806648 + 5.96153846 = 6.696345108 x = 6.696345108 Simplifying x = 6.696345108Subproblem 2
x + -5.96153846 = -0.734806648 Simplifying x + -5.96153846 = -0.734806648 Reorder the terms: -5.96153846 + x = -0.734806648 Solving -5.96153846 + x = -0.734806648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.96153846' to each side of the equation. -5.96153846 + 5.96153846 + x = -0.734806648 + 5.96153846 Combine like terms: -5.96153846 + 5.96153846 = 0.00000000 0.00000000 + x = -0.734806648 + 5.96153846 x = -0.734806648 + 5.96153846 Combine like terms: -0.734806648 + 5.96153846 = 5.226731812 x = 5.226731812 Simplifying x = 5.226731812Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.696345108, 5.226731812}Solution
x = {6.696345108, 5.226731812}
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