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Simplifying 1.735t2 + 58.9t + -500 = 0 Reorder the terms: -500 + 58.9t + 1.735t2 = 0 Solving -500 + 58.9t + 1.735t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 1.735 the coefficient of the squared term: Divide each side by '1.735'. -288.184438 + 33.9481268t + t2 = 0 Move the constant term to the right: Add '288.184438' to each side of the equation. -288.184438 + 33.9481268t + 288.184438 + t2 = 0 + 288.184438 Reorder the terms: -288.184438 + 288.184438 + 33.9481268t + t2 = 0 + 288.184438 Combine like terms: -288.184438 + 288.184438 = 0.000000 0.000000 + 33.9481268t + t2 = 0 + 288.184438 33.9481268t + t2 = 0 + 288.184438 Combine like terms: 0 + 288.184438 = 288.184438 33.9481268t + t2 = 288.184438 The t term is 33.9481268t. Take half its coefficient (16.9740634). Square it (288.1188283) and add it to both sides. Add '288.1188283' to each side of the equation. 33.9481268t + 288.1188283 + t2 = 288.184438 + 288.1188283 Reorder the terms: 288.1188283 + 33.9481268t + t2 = 288.184438 + 288.1188283 Combine like terms: 288.184438 + 288.1188283 = 576.3032663 288.1188283 + 33.9481268t + t2 = 576.3032663 Factor a perfect square on the left side: (t + 16.9740634)(t + 16.9740634) = 576.3032663 Calculate the square root of the right side: 24.006317217 Break this problem into two subproblems by setting (t + 16.9740634) equal to 24.006317217 and -24.006317217.Subproblem 1
t + 16.9740634 = 24.006317217 Simplifying t + 16.9740634 = 24.006317217 Reorder the terms: 16.9740634 + t = 24.006317217 Solving 16.9740634 + t = 24.006317217 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-16.9740634' to each side of the equation. 16.9740634 + -16.9740634 + t = 24.006317217 + -16.9740634 Combine like terms: 16.9740634 + -16.9740634 = 0.0000000 0.0000000 + t = 24.006317217 + -16.9740634 t = 24.006317217 + -16.9740634 Combine like terms: 24.006317217 + -16.9740634 = 7.032253817 t = 7.032253817 Simplifying t = 7.032253817Subproblem 2
t + 16.9740634 = -24.006317217 Simplifying t + 16.9740634 = -24.006317217 Reorder the terms: 16.9740634 + t = -24.006317217 Solving 16.9740634 + t = -24.006317217 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-16.9740634' to each side of the equation. 16.9740634 + -16.9740634 + t = -24.006317217 + -16.9740634 Combine like terms: 16.9740634 + -16.9740634 = 0.0000000 0.0000000 + t = -24.006317217 + -16.9740634 t = -24.006317217 + -16.9740634 Combine like terms: -24.006317217 + -16.9740634 = -40.980380617 t = -40.980380617 Simplifying t = -40.980380617Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.032253817, -40.980380617}
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