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Simplifying 144 = -16t2 + 64t + -80 Reorder the terms: 144 = -80 + 64t + -16t2 Solving 144 = -80 + 64t + -16t2 Solving for variable 't'. Combine like terms: 144 + 80 = 224 224 + -64t + 16t2 = -80 + 64t + -16t2 + 80 + -64t + 16t2 Reorder the terms: 224 + -64t + 16t2 = -80 + 80 + 64t + -64t + -16t2 + 16t2 Combine like terms: -80 + 80 = 0 224 + -64t + 16t2 = 0 + 64t + -64t + -16t2 + 16t2 224 + -64t + 16t2 = 64t + -64t + -16t2 + 16t2 Combine like terms: 64t + -64t = 0 224 + -64t + 16t2 = 0 + -16t2 + 16t2 224 + -64t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 224 + -64t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(14 + -4t + t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(14 + -4t + t2)' equal to zero and attempt to solve: Simplifying 14 + -4t + t2 = 0 Solving 14 + -4t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + -4t + -14 + t2 = 0 + -14 Reorder the terms: 14 + -14 + -4t + t2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -4t + t2 = 0 + -14 -4t + t2 = 0 + -14 Combine like terms: 0 + -14 = -14 -4t + t2 = -14 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 = -14 + 4 Reorder the terms: 4 + -4t + t2 = -14 + 4 Combine like terms: -14 + 4 = -10 4 + -4t + t2 = -10 Factor a perfect square on the left side: (t + -2)(t + -2) = -10 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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