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Simplifying (2x2 + -4x + -8) + -1(3x2 + 7x + 8) = 0 Reorder the terms: (-8 + -4x + 2x2) + -1(3x2 + 7x + 8) = 0 Remove parenthesis around (-8 + -4x + 2x2) -8 + -4x + 2x2 + -1(3x2 + 7x + 8) = 0 Reorder the terms: -8 + -4x + 2x2 + -1(8 + 7x + 3x2) = 0 -8 + -4x + 2x2 + (8 * -1 + 7x * -1 + 3x2 * -1) = 0 -8 + -4x + 2x2 + (-8 + -7x + -3x2) = 0 Reorder the terms: -8 + -8 + -4x + -7x + 2x2 + -3x2 = 0 Combine like terms: -8 + -8 = -16 -16 + -4x + -7x + 2x2 + -3x2 = 0 Combine like terms: -4x + -7x = -11x -16 + -11x + 2x2 + -3x2 = 0 Combine like terms: 2x2 + -3x2 = -1x2 -16 + -11x + -1x2 = 0 Solving -16 + -11x + -1x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(16 + 11x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(16 + 11x + x2)' equal to zero and attempt to solve: Simplifying 16 + 11x + x2 = 0 Solving 16 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + 11x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + 11x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + 11x + x2 = 0 + -16 11x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 11x + x2 = -16 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 = -16 + 30.25 Reorder the terms: 30.25 + 11x + x2 = -16 + 30.25 Combine like terms: -16 + 30.25 = 14.25 30.25 + 11x + x2 = 14.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (x + 5.5) equal to 3.774917218 and -3.774917218.Subproblem 1
x + 5.5 = 3.774917218 Simplifying x + 5.5 = 3.774917218 Reorder the terms: 5.5 + x = 3.774917218 Solving 5.5 + x = 3.774917218 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 = 3.774917218 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 3.774917218 + -5.5 x = 3.774917218 + -5.5 Combine like terms: 3.774917218 + -5.5 = -1.725082782 x = -1.725082782 Simplifying x = -1.725082782Subproblem 2
x + 5.5 = -3.774917218 Simplifying x + 5.5 = -3.774917218 Reorder the terms: 5.5 + x = -3.774917218 Solving 5.5 + x = -3.774917218 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 = -3.774917218 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -3.774917218 + -5.5 x = -3.774917218 + -5.5 Combine like terms: -3.774917218 + -5.5 = -9.274917218 x = -9.274917218 Simplifying x = -9.274917218Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.725082782, -9.274917218}Solution
x = {-1.725082782, -9.274917218}
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