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Simplifying 0.1t2 + 20t + 660 = 0 Reorder the terms: 660 + 20t + 0.1t2 = 0 Solving 660 + 20t + 0.1t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. 6600 + 200t + t2 = 0 Move the constant term to the right: Add '-6600' to each side of the equation. 6600 + 200t + -6600 + t2 = 0 + -6600 Reorder the terms: 6600 + -6600 + 200t + t2 = 0 + -6600 Combine like terms: 6600 + -6600 = 0 0 + 200t + t2 = 0 + -6600 200t + t2 = 0 + -6600 Combine like terms: 0 + -6600 = -6600 200t + t2 = -6600 The t term is 200t. Take half its coefficient (100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. 200t + 10000 + t2 = -6600 + 10000 Reorder the terms: 10000 + 200t + t2 = -6600 + 10000 Combine like terms: -6600 + 10000 = 3400 10000 + 200t + t2 = 3400 Factor a perfect square on the left side: (t + 100)(t + 100) = 3400 Calculate the square root of the right side: 58.309518948 Break this problem into two subproblems by setting (t + 100) equal to 58.309518948 and -58.309518948.Subproblem 1
t + 100 = 58.309518948 Simplifying t + 100 = 58.309518948 Reorder the terms: 100 + t = 58.309518948 Solving 100 + t = 58.309518948 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + t = 58.309518948 + -100 Combine like terms: 100 + -100 = 0 0 + t = 58.309518948 + -100 t = 58.309518948 + -100 Combine like terms: 58.309518948 + -100 = -41.690481052 t = -41.690481052 Simplifying t = -41.690481052Subproblem 2
t + 100 = -58.309518948 Simplifying t + 100 = -58.309518948 Reorder the terms: 100 + t = -58.309518948 Solving 100 + t = -58.309518948 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + t = -58.309518948 + -100 Combine like terms: 100 + -100 = 0 0 + t = -58.309518948 + -100 t = -58.309518948 + -100 Combine like terms: -58.309518948 + -100 = -158.309518948 t = -158.309518948 Simplifying t = -158.309518948Solution
The solution to the problem is based on the solutions from the subproblems. t = {-41.690481052, -158.309518948}
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