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Simplifying 0 = -16t2 + 144t + 16 Reorder the terms: 0 = 16 + 144t + -16t2 Solving 0 = 16 + 144t + -16t2 Solving for variable 't'. Combine like terms: 0 + -16 = -16 -16 + -144t + 16t2 = 16 + 144t + -16t2 + -16 + -144t + 16t2 Reorder the terms: -16 + -144t + 16t2 = 16 + -16 + 144t + -144t + -16t2 + 16t2 Combine like terms: 16 + -16 = 0 -16 + -144t + 16t2 = 0 + 144t + -144t + -16t2 + 16t2 -16 + -144t + 16t2 = 144t + -144t + -16t2 + 16t2 Combine like terms: 144t + -144t = 0 -16 + -144t + 16t2 = 0 + -16t2 + 16t2 -16 + -144t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -16 + -144t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-1 + -9t + t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-1 + -9t + t2)' equal to zero and attempt to solve: Simplifying -1 + -9t + t2 = 0 Solving -1 + -9t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -9t + 1 + t2 = 0 + 1 Reorder the terms: -1 + 1 + -9t + t2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -9t + t2 = 0 + 1 -9t + t2 = 0 + 1 Combine like terms: 0 + 1 = 1 -9t + t2 = 1 The t term is -9t. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9t + 20.25 + t2 = 1 + 20.25 Reorder the terms: 20.25 + -9t + t2 = 1 + 20.25 Combine like terms: 1 + 20.25 = 21.25 20.25 + -9t + t2 = 21.25 Factor a perfect square on the left side: (t + -4.5)(t + -4.5) = 21.25 Calculate the square root of the right side: 4.609772229 Break this problem into two subproblems by setting (t + -4.5) equal to 4.609772229 and -4.609772229.Subproblem 1
t + -4.5 = 4.609772229 Simplifying t + -4.5 = 4.609772229 Reorder the terms: -4.5 + t = 4.609772229 Solving -4.5 + t = 4.609772229 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + t = 4.609772229 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + t = 4.609772229 + 4.5 t = 4.609772229 + 4.5 Combine like terms: 4.609772229 + 4.5 = 9.109772229 t = 9.109772229 Simplifying t = 9.109772229Subproblem 2
t + -4.5 = -4.609772229 Simplifying t + -4.5 = -4.609772229 Reorder the terms: -4.5 + t = -4.609772229 Solving -4.5 + t = -4.609772229 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + t = -4.609772229 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + t = -4.609772229 + 4.5 t = -4.609772229 + 4.5 Combine like terms: -4.609772229 + 4.5 = -0.109772229 t = -0.109772229 Simplifying t = -0.109772229Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.109772229, -0.109772229}Solution
t = {9.109772229, -0.109772229}
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