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Simplifying 2x2 + -26x + 6 = 0 Reorder the terms: 6 + -26x + 2x2 = 0 Solving 6 + -26x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + -13x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -13x + x2)' equal to zero and attempt to solve: Simplifying 3 + -13x + x2 = 0 Solving 3 + -13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -13x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -13x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -13x + x2 = 0 + -3 -13x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -13x + x2 = -3 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = -3 + 42.25 Reorder the terms: 42.25 + -13x + x2 = -3 + 42.25 Combine like terms: -3 + 42.25 = 39.25 42.25 + -13x + x2 = 39.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 39.25 Calculate the square root of the right side: 6.264982043 Break this problem into two subproblems by setting (x + -6.5) equal to 6.264982043 and -6.264982043.Subproblem 1
x + -6.5 = 6.264982043 Simplifying x + -6.5 = 6.264982043 Reorder the terms: -6.5 + x = 6.264982043 Solving -6.5 + x = 6.264982043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 6.264982043 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 6.264982043 + 6.5 x = 6.264982043 + 6.5 Combine like terms: 6.264982043 + 6.5 = 12.764982043 x = 12.764982043 Simplifying x = 12.764982043Subproblem 2
x + -6.5 = -6.264982043 Simplifying x + -6.5 = -6.264982043 Reorder the terms: -6.5 + x = -6.264982043 Solving -6.5 + x = -6.264982043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -6.264982043 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -6.264982043 + 6.5 x = -6.264982043 + 6.5 Combine like terms: -6.264982043 + 6.5 = 0.235017957 x = 0.235017957 Simplifying x = 0.235017957Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.764982043, 0.235017957}Solution
x = {12.764982043, 0.235017957}
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