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Simplifying 80 = 5t2 + -100t Reorder the terms: 80 = -100t + 5t2 Solving 80 = -100t + 5t2 Solving for variable 't'. Reorder the terms: 80 + 100t + -5t2 = -100t + 100t + 5t2 + -5t2 Combine like terms: -100t + 100t = 0 80 + 100t + -5t2 = 0 + 5t2 + -5t2 80 + 100t + -5t2 = 5t2 + -5t2 Combine like terms: 5t2 + -5t2 = 0 80 + 100t + -5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(16 + 20t + -1t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(16 + 20t + -1t2)' equal to zero and attempt to solve: Simplifying 16 + 20t + -1t2 = 0 Solving 16 + 20t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -16 + -20t + t2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + -20t + 16 + t2 = 0 + 16 Reorder the terms: -16 + 16 + -20t + t2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -20t + t2 = 0 + 16 -20t + t2 = 0 + 16 Combine like terms: 0 + 16 = 16 -20t + t2 = 16 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 = 16 + 100 Reorder the terms: 100 + -20t + t2 = 16 + 100 Combine like terms: 16 + 100 = 116 100 + -20t + t2 = 116 Factor a perfect square on the left side: (t + -10)(t + -10) = 116 Calculate the square root of the right side: 10.770329614 Break this problem into two subproblems by setting (t + -10) equal to 10.770329614 and -10.770329614.Subproblem 1
t + -10 = 10.770329614 Simplifying t + -10 = 10.770329614 Reorder the terms: -10 + t = 10.770329614 Solving -10 + t = 10.770329614 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 = 10.770329614 + 10 Combine like terms: -10 + 10 = 0 0 + t = 10.770329614 + 10 t = 10.770329614 + 10 Combine like terms: 10.770329614 + 10 = 20.770329614 t = 20.770329614 Simplifying t = 20.770329614Subproblem 2
t + -10 = -10.770329614 Simplifying t + -10 = -10.770329614 Reorder the terms: -10 + t = -10.770329614 Solving -10 + t = -10.770329614 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 = -10.770329614 + 10 Combine like terms: -10 + 10 = 0 0 + t = -10.770329614 + 10 t = -10.770329614 + 10 Combine like terms: -10.770329614 + 10 = -0.770329614 t = -0.770329614 Simplifying t = -0.770329614Solution
The solution to the problem is based on the solutions from the subproblems. t = {20.770329614, -0.770329614}Solution
t = {20.770329614, -0.770329614}
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