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Simplifying 4x2 + 36x + -32 = 0 Reorder the terms: -32 + 36x + 4x2 = 0 Solving -32 + 36x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-8 + 9x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-8 + 9x + x2)' equal to zero and attempt to solve: Simplifying -8 + 9x + x2 = 0 Solving -8 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 9x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 9x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 9x + x2 = 0 + 8 9x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 9x + x2 = 8 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 8 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 8 + 20.25 Combine like terms: 8 + 20.25 = 28.25 20.25 + 9x + x2 = 28.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 28.25 Calculate the square root of the right side: 5.315072906 Break this problem into two subproblems by setting (x + 4.5) equal to 5.315072906 and -5.315072906.Subproblem 1
x + 4.5 = 5.315072906 Simplifying x + 4.5 = 5.315072906 Reorder the terms: 4.5 + x = 5.315072906 Solving 4.5 + x = 5.315072906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 5.315072906 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 5.315072906 + -4.5 x = 5.315072906 + -4.5 Combine like terms: 5.315072906 + -4.5 = 0.815072906 x = 0.815072906 Simplifying x = 0.815072906Subproblem 2
x + 4.5 = -5.315072906 Simplifying x + 4.5 = -5.315072906 Reorder the terms: 4.5 + x = -5.315072906 Solving 4.5 + x = -5.315072906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -5.315072906 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -5.315072906 + -4.5 x = -5.315072906 + -4.5 Combine like terms: -5.315072906 + -4.5 = -9.815072906 x = -9.815072906 Simplifying x = -9.815072906Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.815072906, -9.815072906}Solution
x = {0.815072906, -9.815072906}
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