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Simplifying 0 = 16t2 + -640t + -6400 Reorder the terms: 0 = -6400 + -640t + 16t2 Solving 0 = -6400 + -640t + 16t2 Solving for variable 't'. Combine like terms: 0 + 6400 = 6400 6400 + 640t + -16t2 = -6400 + -640t + 16t2 + 6400 + 640t + -16t2 Reorder the terms: 6400 + 640t + -16t2 = -6400 + 6400 + -640t + 640t + 16t2 + -16t2 Combine like terms: -6400 + 6400 = 0 6400 + 640t + -16t2 = 0 + -640t + 640t + 16t2 + -16t2 6400 + 640t + -16t2 = -640t + 640t + 16t2 + -16t2 Combine like terms: -640t + 640t = 0 6400 + 640t + -16t2 = 0 + 16t2 + -16t2 6400 + 640t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 6400 + 640t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(400 + 40t + -1t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(400 + 40t + -1t2)' equal to zero and attempt to solve: Simplifying 400 + 40t + -1t2 = 0 Solving 400 + 40t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -400 + -40t + t2 = 0 Move the constant term to the right: Add '400' to each side of the equation. -400 + -40t + 400 + t2 = 0 + 400 Reorder the terms: -400 + 400 + -40t + t2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + -40t + t2 = 0 + 400 -40t + t2 = 0 + 400 Combine like terms: 0 + 400 = 400 -40t + t2 = 400 The t term is -40t. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40t + 400 + t2 = 400 + 400 Reorder the terms: 400 + -40t + t2 = 400 + 400 Combine like terms: 400 + 400 = 800 400 + -40t + t2 = 800 Factor a perfect square on the left side: (t + -20)(t + -20) = 800 Calculate the square root of the right side: 28.284271247 Break this problem into two subproblems by setting (t + -20) equal to 28.284271247 and -28.284271247.Subproblem 1
t + -20 = 28.284271247 Simplifying t + -20 = 28.284271247 Reorder the terms: -20 + t = 28.284271247 Solving -20 + t = 28.284271247 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + t = 28.284271247 + 20 Combine like terms: -20 + 20 = 0 0 + t = 28.284271247 + 20 t = 28.284271247 + 20 Combine like terms: 28.284271247 + 20 = 48.284271247 t = 48.284271247 Simplifying t = 48.284271247Subproblem 2
t + -20 = -28.284271247 Simplifying t + -20 = -28.284271247 Reorder the terms: -20 + t = -28.284271247 Solving -20 + t = -28.284271247 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + t = -28.284271247 + 20 Combine like terms: -20 + 20 = 0 0 + t = -28.284271247 + 20 t = -28.284271247 + 20 Combine like terms: -28.284271247 + 20 = -8.284271247 t = -8.284271247 Simplifying t = -8.284271247Solution
The solution to the problem is based on the solutions from the subproblems. t = {48.284271247, -8.284271247}Solution
t = {48.284271247, -8.284271247}
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