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Simplifying 2x2 + 24x + -40 = 0 Reorder the terms: -40 + 24x + 2x2 = 0 Solving -40 + 24x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-20 + 12x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-20 + 12x + x2)' equal to zero and attempt to solve: Simplifying -20 + 12x + x2 = 0 Solving -20 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + 12x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + 12x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 12x + x2 = 0 + 20 12x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 12x + x2 = 20 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 20 + 36 Reorder the terms: 36 + 12x + x2 = 20 + 36 Combine like terms: 20 + 36 = 56 36 + 12x + x2 = 56 Factor a perfect square on the left side: (x + 6)(x + 6) = 56 Calculate the square root of the right side: 7.483314774 Break this problem into two subproblems by setting (x + 6) equal to 7.483314774 and -7.483314774.Subproblem 1
x + 6 = 7.483314774 Simplifying x + 6 = 7.483314774 Reorder the terms: 6 + x = 7.483314774 Solving 6 + x = 7.483314774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 7.483314774 + -6 Combine like terms: 6 + -6 = 0 0 + x = 7.483314774 + -6 x = 7.483314774 + -6 Combine like terms: 7.483314774 + -6 = 1.483314774 x = 1.483314774 Simplifying x = 1.483314774Subproblem 2
x + 6 = -7.483314774 Simplifying x + 6 = -7.483314774 Reorder the terms: 6 + x = -7.483314774 Solving 6 + x = -7.483314774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -7.483314774 + -6 Combine like terms: 6 + -6 = 0 0 + x = -7.483314774 + -6 x = -7.483314774 + -6 Combine like terms: -7.483314774 + -6 = -13.483314774 x = -13.483314774 Simplifying x = -13.483314774Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.483314774, -13.483314774}Solution
x = {1.483314774, -13.483314774}
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