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Simplifying 68 = -16t2 + -64t + -12 Reorder the terms: 68 = -12 + -64t + -16t2 Solving 68 = -12 + -64t + -16t2 Solving for variable 't'. Combine like terms: 68 + 12 = 80 80 + 64t + 16t2 = -12 + -64t + -16t2 + 12 + 64t + 16t2 Reorder the terms: 80 + 64t + 16t2 = -12 + 12 + -64t + 64t + -16t2 + 16t2 Combine like terms: -12 + 12 = 0 80 + 64t + 16t2 = 0 + -64t + 64t + -16t2 + 16t2 80 + 64t + 16t2 = -64t + 64t + -16t2 + 16t2 Combine like terms: -64t + 64t = 0 80 + 64t + 16t2 = 0 + -16t2 + 16t2 80 + 64t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 80 + 64t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(5 + 4t + t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(5 + 4t + t2)' equal to zero and attempt to solve: Simplifying 5 + 4t + t2 = 0 Solving 5 + 4t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 4t + -5 + t2 = 0 + -5 Reorder the terms: 5 + -5 + 4t + t2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4t + t2 = 0 + -5 4t + t2 = 0 + -5 Combine like terms: 0 + -5 = -5 4t + t2 = -5 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 = -5 + 4 Reorder the terms: 4 + 4t + t2 = -5 + 4 Combine like terms: -5 + 4 = -1 4 + 4t + t2 = -1 Factor a perfect square on the left side: (t + 2)(t + 2) = -1 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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