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Simplifying 0 = 16t2 + 64t + 192 Reorder the terms: 0 = 192 + 64t + 16t2 Solving 0 = 192 + 64t + 16t2 Solving for variable 't'. Combine like terms: 0 + -192 = -192 -192 + -64t + -16t2 = 192 + 64t + 16t2 + -192 + -64t + -16t2 Reorder the terms: -192 + -64t + -16t2 = 192 + -192 + 64t + -64t + 16t2 + -16t2 Combine like terms: 192 + -192 = 0 -192 + -64t + -16t2 = 0 + 64t + -64t + 16t2 + -16t2 -192 + -64t + -16t2 = 64t + -64t + 16t2 + -16t2 Combine like terms: 64t + -64t = 0 -192 + -64t + -16t2 = 0 + 16t2 + -16t2 -192 + -64t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -192 + -64t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-16'. -16(12 + 4t + t2) = 0 Ignore the factor -16.Subproblem 1
Set the factor '(12 + 4t + t2)' equal to zero and attempt to solve: Simplifying 12 + 4t + t2 = 0 Solving 12 + 4t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + 4t + -12 + t2 = 0 + -12 Reorder the terms: 12 + -12 + 4t + t2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 4t + t2 = 0 + -12 4t + t2 = 0 + -12 Combine like terms: 0 + -12 = -12 4t + t2 = -12 The t term is 4t. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4t + 4 + t2 = -12 + 4 Reorder the terms: 4 + 4t + t2 = -12 + 4 Combine like terms: -12 + 4 = -8 4 + 4t + t2 = -8 Factor a perfect square on the left side: (t + 2)(t + 2) = -8 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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