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Simplifying 26 = 2(x + -6)(x + 3) Reorder the terms: 26 = 2(-6 + x)(x + 3) Reorder the terms: 26 = 2(-6 + x)(3 + x) Multiply (-6 + x) * (3 + x) 26 = 2(-6(3 + x) + x(3 + x)) 26 = 2((3 * -6 + x * -6) + x(3 + x)) 26 = 2((-18 + -6x) + x(3 + x)) 26 = 2(-18 + -6x + (3 * x + x * x)) 26 = 2(-18 + -6x + (3x + x2)) Combine like terms: -6x + 3x = -3x 26 = 2(-18 + -3x + x2) 26 = (-18 * 2 + -3x * 2 + x2 * 2) 26 = (-36 + -6x + 2x2) Solving 26 = -36 + -6x + 2x2 Solving for variable 'x'. Combine like terms: 26 + 36 = 62 62 + 6x + -2x2 = -36 + -6x + 2x2 + 36 + 6x + -2x2 Reorder the terms: 62 + 6x + -2x2 = -36 + 36 + -6x + 6x + 2x2 + -2x2 Combine like terms: -36 + 36 = 0 62 + 6x + -2x2 = 0 + -6x + 6x + 2x2 + -2x2 62 + 6x + -2x2 = -6x + 6x + 2x2 + -2x2 Combine like terms: -6x + 6x = 0 62 + 6x + -2x2 = 0 + 2x2 + -2x2 62 + 6x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 62 + 6x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(31 + 3x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(31 + 3x + -1x2)' equal to zero and attempt to solve: Simplifying 31 + 3x + -1x2 = 0 Solving 31 + 3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -31 + -3x + x2 = 0 Move the constant term to the right: Add '31' to each side of the equation. -31 + -3x + 31 + x2 = 0 + 31 Reorder the terms: -31 + 31 + -3x + x2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + -3x + x2 = 0 + 31 -3x + x2 = 0 + 31 Combine like terms: 0 + 31 = 31 -3x + x2 = 31 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 31 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 31 + 2.25 Combine like terms: 31 + 2.25 = 33.25 2.25 + -3x + x2 = 33.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 33.25 Calculate the square root of the right side: 5.766281297 Break this problem into two subproblems by setting (x + -1.5) equal to 5.766281297 and -5.766281297.Subproblem 1
x + -1.5 = 5.766281297 Simplifying x + -1.5 = 5.766281297 Reorder the terms: -1.5 + x = 5.766281297 Solving -1.5 + x = 5.766281297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 5.766281297 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 5.766281297 + 1.5 x = 5.766281297 + 1.5 Combine like terms: 5.766281297 + 1.5 = 7.266281297 x = 7.266281297 Simplifying x = 7.266281297Subproblem 2
x + -1.5 = -5.766281297 Simplifying x + -1.5 = -5.766281297 Reorder the terms: -1.5 + x = -5.766281297 Solving -1.5 + x = -5.766281297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -5.766281297 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -5.766281297 + 1.5 x = -5.766281297 + 1.5 Combine like terms: -5.766281297 + 1.5 = -4.266281297 x = -4.266281297 Simplifying x = -4.266281297Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.266281297, -4.266281297}Solution
x = {7.266281297, -4.266281297}
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