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Simplifying 3x2 + 72x + 192 = 0 Reorder the terms: 192 + 72x + 3x2 = 0 Solving 192 + 72x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(64 + 24x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(64 + 24x + x2)' equal to zero and attempt to solve: Simplifying 64 + 24x + x2 = 0 Solving 64 + 24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-64' to each side of the equation. 64 + 24x + -64 + x2 = 0 + -64 Reorder the terms: 64 + -64 + 24x + x2 = 0 + -64 Combine like terms: 64 + -64 = 0 0 + 24x + x2 = 0 + -64 24x + x2 = 0 + -64 Combine like terms: 0 + -64 = -64 24x + x2 = -64 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 = -64 + 144 Reorder the terms: 144 + 24x + x2 = -64 + 144 Combine like terms: -64 + 144 = 80 144 + 24x + x2 = 80 Factor a perfect square on the left side: (x + 12)(x + 12) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (x + 12) equal to 8.94427191 and -8.94427191.Subproblem 1
x + 12 = 8.94427191 Simplifying x + 12 = 8.94427191 Reorder the terms: 12 + x = 8.94427191 Solving 12 + x = 8.94427191 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 = 8.94427191 + -12 Combine like terms: 12 + -12 = 0 0 + x = 8.94427191 + -12 x = 8.94427191 + -12 Combine like terms: 8.94427191 + -12 = -3.05572809 x = -3.05572809 Simplifying x = -3.05572809Subproblem 2
x + 12 = -8.94427191 Simplifying x + 12 = -8.94427191 Reorder the terms: 12 + x = -8.94427191 Solving 12 + x = -8.94427191 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 = -8.94427191 + -12 Combine like terms: 12 + -12 = 0 0 + x = -8.94427191 + -12 x = -8.94427191 + -12 Combine like terms: -8.94427191 + -12 = -20.94427191 x = -20.94427191 Simplifying x = -20.94427191Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.05572809, -20.94427191}Solution
x = {-3.05572809, -20.94427191}
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