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Simplifying -5t2 + 100t + 20 = 0 Reorder the terms: 20 + 100t + -5t2 = 0 Solving 20 + 100t + -5t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '5'. 5(4 + 20t + -1t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(4 + 20t + -1t2)' equal to zero and attempt to solve: Simplifying 4 + 20t + -1t2 = 0 Solving 4 + 20t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + -20t + t2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -20t + 4 + t2 = 0 + 4 Reorder the terms: -4 + 4 + -20t + t2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -20t + t2 = 0 + 4 -20t + t2 = 0 + 4 Combine like terms: 0 + 4 = 4 -20t + t2 = 4 The t term is -20t. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20t + 100 + t2 = 4 + 100 Reorder the terms: 100 + -20t + t2 = 4 + 100 Combine like terms: 4 + 100 = 104 100 + -20t + t2 = 104 Factor a perfect square on the left side: (t + -10)(t + -10) = 104 Calculate the square root of the right side: 10.198039027 Break this problem into two subproblems by setting (t + -10) equal to 10.198039027 and -10.198039027.Subproblem 1
t + -10 = 10.198039027 Simplifying t + -10 = 10.198039027 Reorder the terms: -10 + t = 10.198039027 Solving -10 + t = 10.198039027 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + t = 10.198039027 + 10 Combine like terms: -10 + 10 = 0 0 + t = 10.198039027 + 10 t = 10.198039027 + 10 Combine like terms: 10.198039027 + 10 = 20.198039027 t = 20.198039027 Simplifying t = 20.198039027Subproblem 2
t + -10 = -10.198039027 Simplifying t + -10 = -10.198039027 Reorder the terms: -10 + t = -10.198039027 Solving -10 + t = -10.198039027 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + t = -10.198039027 + 10 Combine like terms: -10 + 10 = 0 0 + t = -10.198039027 + 10 t = -10.198039027 + 10 Combine like terms: -10.198039027 + 10 = -0.198039027 t = -0.198039027 Simplifying t = -0.198039027Solution
The solution to the problem is based on the solutions from the subproblems. t = {20.198039027, -0.198039027}Solution
t = {20.198039027, -0.198039027}
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