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Simplifying -2x2 + -18x + 26 = 0 Reorder the terms: 26 + -18x + -2x2 = 0 Solving 26 + -18x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(13 + -9x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(13 + -9x + -1x2)' equal to zero and attempt to solve: Simplifying 13 + -9x + -1x2 = 0 Solving 13 + -9x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -13 + 9x + x2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + 9x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + 9x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 9x + x2 = 0 + 13 9x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 9x + x2 = 13 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 13 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 13 + 20.25 Combine like terms: 13 + 20.25 = 33.25 20.25 + 9x + x2 = 33.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 33.25 Calculate the square root of the right side: 5.766281297 Break this problem into two subproblems by setting (x + 4.5) equal to 5.766281297 and -5.766281297.Subproblem 1
x + 4.5 = 5.766281297 Simplifying x + 4.5 = 5.766281297 Reorder the terms: 4.5 + x = 5.766281297 Solving 4.5 + x = 5.766281297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 5.766281297 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 5.766281297 + -4.5 x = 5.766281297 + -4.5 Combine like terms: 5.766281297 + -4.5 = 1.266281297 x = 1.266281297 Simplifying x = 1.266281297Subproblem 2
x + 4.5 = -5.766281297 Simplifying x + 4.5 = -5.766281297 Reorder the terms: 4.5 + x = -5.766281297 Solving 4.5 + x = -5.766281297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -5.766281297 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -5.766281297 + -4.5 x = -5.766281297 + -4.5 Combine like terms: -5.766281297 + -4.5 = -10.266281297 x = -10.266281297 Simplifying x = -10.266281297Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.266281297, -10.266281297}Solution
x = {1.266281297, -10.266281297}
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