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Simplifying 6x2 + 36x + 192 = 0 Reorder the terms: 192 + 36x + 6x2 = 0 Solving 192 + 36x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(32 + 6x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(32 + 6x + x2)' equal to zero and attempt to solve: Simplifying 32 + 6x + x2 = 0 Solving 32 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-32' to each side of the equation. 32 + 6x + -32 + x2 = 0 + -32 Reorder the terms: 32 + -32 + 6x + x2 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + 6x + x2 = 0 + -32 6x + x2 = 0 + -32 Combine like terms: 0 + -32 = -32 6x + x2 = -32 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = -32 + 9 Reorder the terms: 9 + 6x + x2 = -32 + 9 Combine like terms: -32 + 9 = -23 9 + 6x + x2 = -23 Factor a perfect square on the left side: (x + 3)(x + 3) = -23 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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