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Simplifying 0 = -16t2 + 1900t + 100 Reorder the terms: 0 = 100 + 1900t + -16t2 Solving 0 = 100 + 1900t + -16t2 Solving for variable 't'. Combine like terms: 0 + -100 = -100 -100 + -1900t + 16t2 = 100 + 1900t + -16t2 + -100 + -1900t + 16t2 Reorder the terms: -100 + -1900t + 16t2 = 100 + -100 + 1900t + -1900t + -16t2 + 16t2 Combine like terms: 100 + -100 = 0 -100 + -1900t + 16t2 = 0 + 1900t + -1900t + -16t2 + 16t2 -100 + -1900t + 16t2 = 1900t + -1900t + -16t2 + 16t2 Combine like terms: 1900t + -1900t = 0 -100 + -1900t + 16t2 = 0 + -16t2 + 16t2 -100 + -1900t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -100 + -1900t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-25 + -475t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-25 + -475t + 4t2)' equal to zero and attempt to solve: Simplifying -25 + -475t + 4t2 = 0 Solving -25 + -475t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6.25 + -118.75t + t2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + -118.75t + 6.25 + t2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + -118.75t + t2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + -118.75t + t2 = 0 + 6.25 -118.75t + t2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 -118.75t + t2 = 6.25 The t term is -118.75t. Take half its coefficient (-59.375). Square it (3525.390625) and add it to both sides. Add '3525.390625' to each side of the equation. -118.75t + 3525.390625 + t2 = 6.25 + 3525.390625 Reorder the terms: 3525.390625 + -118.75t + t2 = 6.25 + 3525.390625 Combine like terms: 6.25 + 3525.390625 = 3531.640625 3525.390625 + -118.75t + t2 = 3531.640625 Factor a perfect square on the left side: (t + -59.375)(t + -59.375) = 3531.640625 Calculate the square root of the right side: 59.427608273 Break this problem into two subproblems by setting (t + -59.375) equal to 59.427608273 and -59.427608273.Subproblem 1
t + -59.375 = 59.427608273 Simplifying t + -59.375 = 59.427608273 Reorder the terms: -59.375 + t = 59.427608273 Solving -59.375 + t = 59.427608273 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '59.375' to each side of the equation. -59.375 + 59.375 + t = 59.427608273 + 59.375 Combine like terms: -59.375 + 59.375 = 0.000 0.000 + t = 59.427608273 + 59.375 t = 59.427608273 + 59.375 Combine like terms: 59.427608273 + 59.375 = 118.802608273 t = 118.802608273 Simplifying t = 118.802608273Subproblem 2
t + -59.375 = -59.427608273 Simplifying t + -59.375 = -59.427608273 Reorder the terms: -59.375 + t = -59.427608273 Solving -59.375 + t = -59.427608273 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '59.375' to each side of the equation. -59.375 + 59.375 + t = -59.427608273 + 59.375 Combine like terms: -59.375 + 59.375 = 0.000 0.000 + t = -59.427608273 + 59.375 t = -59.427608273 + 59.375 Combine like terms: -59.427608273 + 59.375 = -0.052608273 t = -0.052608273 Simplifying t = -0.052608273Solution
The solution to the problem is based on the solutions from the subproblems. t = {118.802608273, -0.052608273}Solution
t = {118.802608273, -0.052608273}
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