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Simplifying 4x2 + 96x + 144 = 0 Reorder the terms: 144 + 96x + 4x2 = 0 Solving 144 + 96x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(36 + 24x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(36 + 24x + x2)' equal to zero and attempt to solve: Simplifying 36 + 24x + x2 = 0 Solving 36 + 24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + 24x + -36 + x2 = 0 + -36 Reorder the terms: 36 + -36 + 24x + x2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + 24x + x2 = 0 + -36 24x + x2 = 0 + -36 Combine like terms: 0 + -36 = -36 24x + x2 = -36 The x term is 24x. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x + 144 + x2 = -36 + 144 Reorder the terms: 144 + 24x + x2 = -36 + 144 Combine like terms: -36 + 144 = 108 144 + 24x + x2 = 108 Factor a perfect square on the left side: (x + 12)(x + 12) = 108 Calculate the square root of the right side: 10.392304845 Break this problem into two subproblems by setting (x + 12) equal to 10.392304845 and -10.392304845.Subproblem 1
x + 12 = 10.392304845 Simplifying x + 12 = 10.392304845 Reorder the terms: 12 + x = 10.392304845 Solving 12 + x = 10.392304845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 10.392304845 + -12 Combine like terms: 12 + -12 = 0 0 + x = 10.392304845 + -12 x = 10.392304845 + -12 Combine like terms: 10.392304845 + -12 = -1.607695155 x = -1.607695155 Simplifying x = -1.607695155Subproblem 2
x + 12 = -10.392304845 Simplifying x + 12 = -10.392304845 Reorder the terms: 12 + x = -10.392304845 Solving 12 + x = -10.392304845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -10.392304845 + -12 Combine like terms: 12 + -12 = 0 0 + x = -10.392304845 + -12 x = -10.392304845 + -12 Combine like terms: -10.392304845 + -12 = -22.392304845 x = -22.392304845 Simplifying x = -22.392304845Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.607695155, -22.392304845}Solution
x = {-1.607695155, -22.392304845}
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