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Simplifying 9 = 20t + -5t2 Solving 9 = 20t + -5t2 Solving for variable 't'. Reorder the terms: 9 + -20t + 5t2 = 20t + -20t + -5t2 + 5t2 Combine like terms: 20t + -20t = 0 9 + -20t + 5t2 = 0 + -5t2 + 5t2 9 + -20t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 9 + -20t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.8 + -4t + t2 = 0 Move the constant term to the right: Add '-1.8' to each side of the equation. 1.8 + -4t + -1.8 + t2 = 0 + -1.8 Reorder the terms: 1.8 + -1.8 + -4t + t2 = 0 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + -4t + t2 = 0 + -1.8 -4t + t2 = 0 + -1.8 Combine like terms: 0 + -1.8 = -1.8 -4t + t2 = -1.8 The t term is -4t. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4t + 4 + t2 = -1.8 + 4 Reorder the terms: 4 + -4t + t2 = -1.8 + 4 Combine like terms: -1.8 + 4 = 2.2 4 + -4t + t2 = 2.2 Factor a perfect square on the left side: (t + -2)(t + -2) = 2.2 Calculate the square root of the right side: 1.483239697 Break this problem into two subproblems by setting (t + -2) equal to 1.483239697 and -1.483239697.Subproblem 1
t + -2 = 1.483239697 Simplifying t + -2 = 1.483239697 Reorder the terms: -2 + t = 1.483239697 Solving -2 + t = 1.483239697 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 1.483239697 + 2 Combine like terms: -2 + 2 = 0 0 + t = 1.483239697 + 2 t = 1.483239697 + 2 Combine like terms: 1.483239697 + 2 = 3.483239697 t = 3.483239697 Simplifying t = 3.483239697Subproblem 2
t + -2 = -1.483239697 Simplifying t + -2 = -1.483239697 Reorder the terms: -2 + t = -1.483239697 Solving -2 + t = -1.483239697 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -1.483239697 + 2 Combine like terms: -2 + 2 = 0 0 + t = -1.483239697 + 2 t = -1.483239697 + 2 Combine like terms: -1.483239697 + 2 = 0.516760303 t = 0.516760303 Simplifying t = 0.516760303Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.483239697, 0.516760303}
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