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Simplifying 2x2 + 32x + -6 = 0 Reorder the terms: -6 + 32x + 2x2 = 0 Solving -6 + 32x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 16x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + 16x + x2)' equal to zero and attempt to solve: Simplifying -3 + 16x + x2 = 0 Solving -3 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 16x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 16x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 16x + x2 = 0 + 3 16x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 16x + x2 = 3 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = 3 + 64 Reorder the terms: 64 + 16x + x2 = 3 + 64 Combine like terms: 3 + 64 = 67 64 + 16x + x2 = 67 Factor a perfect square on the left side: (x + 8)(x + 8) = 67 Calculate the square root of the right side: 8.185352772 Break this problem into two subproblems by setting (x + 8) equal to 8.185352772 and -8.185352772.Subproblem 1
x + 8 = 8.185352772 Simplifying x + 8 = 8.185352772 Reorder the terms: 8 + x = 8.185352772 Solving 8 + x = 8.185352772 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 8.185352772 + -8 Combine like terms: 8 + -8 = 0 0 + x = 8.185352772 + -8 x = 8.185352772 + -8 Combine like terms: 8.185352772 + -8 = 0.185352772 x = 0.185352772 Simplifying x = 0.185352772Subproblem 2
x + 8 = -8.185352772 Simplifying x + 8 = -8.185352772 Reorder the terms: 8 + x = -8.185352772 Solving 8 + x = -8.185352772 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -8.185352772 + -8 Combine like terms: 8 + -8 = 0 0 + x = -8.185352772 + -8 x = -8.185352772 + -8 Combine like terms: -8.185352772 + -8 = -16.185352772 x = -16.185352772 Simplifying x = -16.185352772Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.185352772, -16.185352772}Solution
x = {0.185352772, -16.185352772}
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