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Simplifying 0 = x2 + 13x + 26 Reorder the terms: 0 = 26 + 13x + x2 Solving 0 = 26 + 13x + x2 Solving for variable 'x'. Combine like terms: 0 + -26 = -26 -26 + -13x + -1x2 = 26 + 13x + x2 + -26 + -13x + -1x2 Reorder the terms: -26 + -13x + -1x2 = 26 + -26 + 13x + -13x + x2 + -1x2 Combine like terms: 26 + -26 = 0 -26 + -13x + -1x2 = 0 + 13x + -13x + x2 + -1x2 -26 + -13x + -1x2 = 13x + -13x + x2 + -1x2 Combine like terms: 13x + -13x = 0 -26 + -13x + -1x2 = 0 + x2 + -1x2 -26 + -13x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -26 + -13x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(26 + 13x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(26 + 13x + x2)' equal to zero and attempt to solve: Simplifying 26 + 13x + x2 = 0 Solving 26 + 13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-26' to each side of the equation. 26 + 13x + -26 + x2 = 0 + -26 Reorder the terms: 26 + -26 + 13x + x2 = 0 + -26 Combine like terms: 26 + -26 = 0 0 + 13x + x2 = 0 + -26 13x + x2 = 0 + -26 Combine like terms: 0 + -26 = -26 13x + x2 = -26 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 = -26 + 42.25 Reorder the terms: 42.25 + 13x + x2 = -26 + 42.25 Combine like terms: -26 + 42.25 = 16.25 42.25 + 13x + x2 = 16.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (x + 6.5) equal to 4.031128874 and -4.031128874.Subproblem 1
x + 6.5 = 4.031128874 Simplifying x + 6.5 = 4.031128874 Reorder the terms: 6.5 + x = 4.031128874 Solving 6.5 + x = 4.031128874 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 = 4.031128874 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 4.031128874 + -6.5 x = 4.031128874 + -6.5 Combine like terms: 4.031128874 + -6.5 = -2.468871126 x = -2.468871126 Simplifying x = -2.468871126Subproblem 2
x + 6.5 = -4.031128874 Simplifying x + 6.5 = -4.031128874 Reorder the terms: 6.5 + x = -4.031128874 Solving 6.5 + x = -4.031128874 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 = -4.031128874 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -4.031128874 + -6.5 x = -4.031128874 + -6.5 Combine like terms: -4.031128874 + -6.5 = -10.531128874 x = -10.531128874 Simplifying x = -10.531128874Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.468871126, -10.531128874}Solution
x = {-2.468871126, -10.531128874}
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