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Simplifying (4x2 + -8x) + -1(5x2 + 5x) = 2 Reorder the terms: (-8x + 4x2) + -1(5x2 + 5x) = 2 Remove parenthesis around (-8x + 4x2) -8x + 4x2 + -1(5x2 + 5x) = 2 Reorder the terms: -8x + 4x2 + -1(5x + 5x2) = 2 -8x + 4x2 + (5x * -1 + 5x2 * -1) = 2 -8x + 4x2 + (-5x + -5x2) = 2 Reorder the terms: -8x + -5x + 4x2 + -5x2 = 2 Combine like terms: -8x + -5x = -13x -13x + 4x2 + -5x2 = 2 Combine like terms: 4x2 + -5x2 = -1x2 -13x + -1x2 = 2 Solving -13x + -1x2 = 2 Solving for variable 'x'. Reorder the terms: -2 + -13x + -1x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -13x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(2 + 13x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + 13x + x2)' equal to zero and attempt to solve: Simplifying 2 + 13x + x2 = 0 Solving 2 + 13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 13x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 13x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 13x + x2 = 0 + -2 13x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 13x + x2 = -2 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 = -2 + 42.25 Reorder the terms: 42.25 + 13x + x2 = -2 + 42.25 Combine like terms: -2 + 42.25 = 40.25 42.25 + 13x + x2 = 40.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (x + 6.5) equal to 6.34428877 and -6.34428877.Subproblem 1
x + 6.5 = 6.34428877 Simplifying x + 6.5 = 6.34428877 Reorder the terms: 6.5 + x = 6.34428877 Solving 6.5 + x = 6.34428877 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 = 6.34428877 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 6.34428877 + -6.5 x = 6.34428877 + -6.5 Combine like terms: 6.34428877 + -6.5 = -0.15571123 x = -0.15571123 Simplifying x = -0.15571123Subproblem 2
x + 6.5 = -6.34428877 Simplifying x + 6.5 = -6.34428877 Reorder the terms: 6.5 + x = -6.34428877 Solving 6.5 + x = -6.34428877 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 = -6.34428877 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -6.34428877 + -6.5 x = -6.34428877 + -6.5 Combine like terms: -6.34428877 + -6.5 = -12.84428877 x = -12.84428877 Simplifying x = -12.84428877Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.15571123, -12.84428877}Solution
x = {-0.15571123, -12.84428877}
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