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Simplifying 2x2 + 26x + 56 = 0 Reorder the terms: 56 + 26x + 2x2 = 0 Solving 56 + 26x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(28 + 13x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(28 + 13x + x2)' equal to zero and attempt to solve: Simplifying 28 + 13x + x2 = 0 Solving 28 + 13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-28' to each side of the equation. 28 + 13x + -28 + x2 = 0 + -28 Reorder the terms: 28 + -28 + 13x + x2 = 0 + -28 Combine like terms: 28 + -28 = 0 0 + 13x + x2 = 0 + -28 13x + x2 = 0 + -28 Combine like terms: 0 + -28 = -28 13x + x2 = -28 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 = -28 + 42.25 Reorder the terms: 42.25 + 13x + x2 = -28 + 42.25 Combine like terms: -28 + 42.25 = 14.25 42.25 + 13x + x2 = 14.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (x + 6.5) equal to 3.774917218 and -3.774917218.Subproblem 1
x + 6.5 = 3.774917218 Simplifying x + 6.5 = 3.774917218 Reorder the terms: 6.5 + x = 3.774917218 Solving 6.5 + x = 3.774917218 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 = 3.774917218 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 3.774917218 + -6.5 x = 3.774917218 + -6.5 Combine like terms: 3.774917218 + -6.5 = -2.725082782 x = -2.725082782 Simplifying x = -2.725082782Subproblem 2
x + 6.5 = -3.774917218 Simplifying x + 6.5 = -3.774917218 Reorder the terms: 6.5 + x = -3.774917218 Solving 6.5 + x = -3.774917218 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 = -3.774917218 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -3.774917218 + -6.5 x = -3.774917218 + -6.5 Combine like terms: -3.774917218 + -6.5 = -10.274917218 x = -10.274917218 Simplifying x = -10.274917218Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.725082782, -10.274917218}Solution
x = {-2.725082782, -10.274917218}
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