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Simplifying 0 = 16t2 + 64t + 720 Reorder the terms: 0 = 720 + 64t + 16t2 Solving 0 = 720 + 64t + 16t2 Solving for variable 't'. Combine like terms: 0 + -720 = -720 -720 + -64t + -16t2 = 720 + 64t + 16t2 + -720 + -64t + -16t2 Reorder the terms: -720 + -64t + -16t2 = 720 + -720 + 64t + -64t + 16t2 + -16t2 Combine like terms: 720 + -720 = 0 -720 + -64t + -16t2 = 0 + 64t + -64t + 16t2 + -16t2 -720 + -64t + -16t2 = 64t + -64t + 16t2 + -16t2 Combine like terms: 64t + -64t = 0 -720 + -64t + -16t2 = 0 + 16t2 + -16t2 -720 + -64t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -720 + -64t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-16'. -16(45 + 4t + t2) = 0 Ignore the factor -16.Subproblem 1
Set the factor '(45 + 4t + t2)' equal to zero and attempt to solve: Simplifying 45 + 4t + t2 = 0 Solving 45 + 4t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-45' to each side of the equation. 45 + 4t + -45 + t2 = 0 + -45 Reorder the terms: 45 + -45 + 4t + t2 = 0 + -45 Combine like terms: 45 + -45 = 0 0 + 4t + t2 = 0 + -45 4t + t2 = 0 + -45 Combine like terms: 0 + -45 = -45 4t + t2 = -45 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 = -45 + 4 Reorder the terms: 4 + 4t + t2 = -45 + 4 Combine like terms: -45 + 4 = -41 4 + 4t + t2 = -41 Factor a perfect square on the left side: (t + 2)(t + 2) = -41 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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