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Simplifying 2x2 + -12x + -26 = 0 Reorder the terms: -26 + -12x + 2x2 = 0 Solving -26 + -12x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-13 + -6x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-13 + -6x + x2)' equal to zero and attempt to solve: Simplifying -13 + -6x + x2 = 0 Solving -13 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + -6x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + -6x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -6x + x2 = 0 + 13 -6x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 -6x + x2 = 13 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 13 + 9 Reorder the terms: 9 + -6x + x2 = 13 + 9 Combine like terms: 13 + 9 = 22 9 + -6x + x2 = 22 Factor a perfect square on the left side: (x + -3)(x + -3) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (x + -3) equal to 4.69041576 and -4.69041576.Subproblem 1
x + -3 = 4.69041576 Simplifying x + -3 = 4.69041576 Reorder the terms: -3 + x = 4.69041576 Solving -3 + x = 4.69041576 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 4.69041576 + 3 Combine like terms: -3 + 3 = 0 0 + x = 4.69041576 + 3 x = 4.69041576 + 3 Combine like terms: 4.69041576 + 3 = 7.69041576 x = 7.69041576 Simplifying x = 7.69041576Subproblem 2
x + -3 = -4.69041576 Simplifying x + -3 = -4.69041576 Reorder the terms: -3 + x = -4.69041576 Solving -3 + x = -4.69041576 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -4.69041576 + 3 Combine like terms: -3 + 3 = 0 0 + x = -4.69041576 + 3 x = -4.69041576 + 3 Combine like terms: -4.69041576 + 3 = -1.69041576 x = -1.69041576 Simplifying x = -1.69041576Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.69041576, -1.69041576}Solution
x = {7.69041576, -1.69041576}
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