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Simplifying 0 = -16(t2 + -12t + -5) Reorder the terms: 0 = -16(-5 + -12t + t2) 0 = (-5 * -16 + -12t * -16 + t2 * -16) 0 = (80 + 192t + -16t2) Solving 0 = 80 + 192t + -16t2 Solving for variable 't'. Combine like terms: 0 + -80 = -80 -80 + -192t + 16t2 = 80 + 192t + -16t2 + -80 + -192t + 16t2 Reorder the terms: -80 + -192t + 16t2 = 80 + -80 + 192t + -192t + -16t2 + 16t2 Combine like terms: 80 + -80 = 0 -80 + -192t + 16t2 = 0 + 192t + -192t + -16t2 + 16t2 -80 + -192t + 16t2 = 192t + -192t + -16t2 + 16t2 Combine like terms: 192t + -192t = 0 -80 + -192t + 16t2 = 0 + -16t2 + 16t2 -80 + -192t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -80 + -192t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-5 + -12t + t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-5 + -12t + t2)' equal to zero and attempt to solve: Simplifying -5 + -12t + t2 = 0 Solving -5 + -12t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -12t + 5 + t2 = 0 + 5 Reorder the terms: -5 + 5 + -12t + t2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -12t + t2 = 0 + 5 -12t + t2 = 0 + 5 Combine like terms: 0 + 5 = 5 -12t + t2 = 5 The t term is -12t. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12t + 36 + t2 = 5 + 36 Reorder the terms: 36 + -12t + t2 = 5 + 36 Combine like terms: 5 + 36 = 41 36 + -12t + t2 = 41 Factor a perfect square on the left side: (t + -6)(t + -6) = 41 Calculate the square root of the right side: 6.403124237 Break this problem into two subproblems by setting (t + -6) equal to 6.403124237 and -6.403124237.Subproblem 1
t + -6 = 6.403124237 Simplifying t + -6 = 6.403124237 Reorder the terms: -6 + t = 6.403124237 Solving -6 + t = 6.403124237 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + t = 6.403124237 + 6 Combine like terms: -6 + 6 = 0 0 + t = 6.403124237 + 6 t = 6.403124237 + 6 Combine like terms: 6.403124237 + 6 = 12.403124237 t = 12.403124237 Simplifying t = 12.403124237Subproblem 2
t + -6 = -6.403124237 Simplifying t + -6 = -6.403124237 Reorder the terms: -6 + t = -6.403124237 Solving -6 + t = -6.403124237 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + t = -6.403124237 + 6 Combine like terms: -6 + 6 = 0 0 + t = -6.403124237 + 6 t = -6.403124237 + 6 Combine like terms: -6.403124237 + 6 = -0.403124237 t = -0.403124237 Simplifying t = -0.403124237Solution
The solution to the problem is based on the solutions from the subproblems. t = {12.403124237, -0.403124237}Solution
t = {12.403124237, -0.403124237}
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