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Simplifying 16x2 + 144x + 384 = 0 Reorder the terms: 384 + 144x + 16x2 = 0 Solving 384 + 144x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '16'. 16(24 + 9x + x2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(24 + 9x + x2)' equal to zero and attempt to solve: Simplifying 24 + 9x + x2 = 0 Solving 24 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + 9x + -24 + x2 = 0 + -24 Reorder the terms: 24 + -24 + 9x + x2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + 9x + x2 = 0 + -24 9x + x2 = 0 + -24 Combine like terms: 0 + -24 = -24 9x + x2 = -24 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 = -24 + 20.25 Reorder the terms: 20.25 + 9x + x2 = -24 + 20.25 Combine like terms: -24 + 20.25 = -3.75 20.25 + 9x + x2 = -3.75 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = -3.75 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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