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Simplifying 2x2 + 32x + -4 = 0 Reorder the terms: -4 + 32x + 2x2 = 0 Solving -4 + 32x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + 16x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + 16x + x2)' equal to zero and attempt to solve: Simplifying -2 + 16x + x2 = 0 Solving -2 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 16x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 16x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 16x + x2 = 0 + 2 16x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 16x + x2 = 2 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 = 2 + 64 Reorder the terms: 64 + 16x + x2 = 2 + 64 Combine like terms: 2 + 64 = 66 64 + 16x + x2 = 66 Factor a perfect square on the left side: (x + 8)(x + 8) = 66 Calculate the square root of the right side: 8.124038405 Break this problem into two subproblems by setting (x + 8) equal to 8.124038405 and -8.124038405.Subproblem 1
x + 8 = 8.124038405 Simplifying x + 8 = 8.124038405 Reorder the terms: 8 + x = 8.124038405 Solving 8 + x = 8.124038405 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 = 8.124038405 + -8 Combine like terms: 8 + -8 = 0 0 + x = 8.124038405 + -8 x = 8.124038405 + -8 Combine like terms: 8.124038405 + -8 = 0.124038405 x = 0.124038405 Simplifying x = 0.124038405Subproblem 2
x + 8 = -8.124038405 Simplifying x + 8 = -8.124038405 Reorder the terms: 8 + x = -8.124038405 Solving 8 + x = -8.124038405 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 = -8.124038405 + -8 Combine like terms: 8 + -8 = 0 0 + x = -8.124038405 + -8 x = -8.124038405 + -8 Combine like terms: -8.124038405 + -8 = -16.124038405 x = -16.124038405 Simplifying x = -16.124038405Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.124038405, -16.124038405}Solution
x = {0.124038405, -16.124038405}
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