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Simplifying 0 = x2 + 11x + 14 Reorder the terms: 0 = 14 + 11x + x2 Solving 0 = 14 + 11x + x2 Solving for variable 'x'. Combine like terms: 0 + -14 = -14 -14 + -11x + -1x2 = 14 + 11x + x2 + -14 + -11x + -1x2 Reorder the terms: -14 + -11x + -1x2 = 14 + -14 + 11x + -11x + x2 + -1x2 Combine like terms: 14 + -14 = 0 -14 + -11x + -1x2 = 0 + 11x + -11x + x2 + -1x2 -14 + -11x + -1x2 = 11x + -11x + x2 + -1x2 Combine like terms: 11x + -11x = 0 -14 + -11x + -1x2 = 0 + x2 + -1x2 -14 + -11x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -14 + -11x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(14 + 11x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(14 + 11x + x2)' equal to zero and attempt to solve: Simplifying 14 + 11x + x2 = 0 Solving 14 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + 11x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + 11x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 11x + x2 = 0 + -14 11x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 11x + x2 = -14 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = -14 + 30.25 Reorder the terms: 30.25 + 11x + x2 = -14 + 30.25 Combine like terms: -14 + 30.25 = 16.25 30.25 + 11x + x2 = 16.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (x + 5.5) equal to 4.031128874 and -4.031128874.Subproblem 1
x + 5.5 = 4.031128874 Simplifying x + 5.5 = 4.031128874 Reorder the terms: 5.5 + x = 4.031128874 Solving 5.5 + x = 4.031128874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 4.031128874 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 4.031128874 + -5.5 x = 4.031128874 + -5.5 Combine like terms: 4.031128874 + -5.5 = -1.468871126 x = -1.468871126 Simplifying x = -1.468871126Subproblem 2
x + 5.5 = -4.031128874 Simplifying x + 5.5 = -4.031128874 Reorder the terms: 5.5 + x = -4.031128874 Solving 5.5 + x = -4.031128874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -4.031128874 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -4.031128874 + -5.5 x = -4.031128874 + -5.5 Combine like terms: -4.031128874 + -5.5 = -9.531128874 x = -9.531128874 Simplifying x = -9.531128874Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.468871126, -9.531128874}Solution
x = {-1.468871126, -9.531128874}
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