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Simplifying 0.0000987t2 + -0.0101t + 0.0514 = 0 Reorder the terms: 0.0514 + -0.0101t + 0.0000987t2 = 0 Solving 0.0514 + -0.0101t + 0.0000987t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.0000987 the coefficient of the squared term: Divide each side by '0.0000987'. 520.7700101 + -102.3302938t + t2 = 0 Move the constant term to the right: Add '-520.7700101' to each side of the equation. 520.7700101 + -102.3302938t + -520.7700101 + t2 = 0 + -520.7700101 Reorder the terms: 520.7700101 + -520.7700101 + -102.3302938t + t2 = 0 + -520.7700101 Combine like terms: 520.7700101 + -520.7700101 = 0.0000000 0.0000000 + -102.3302938t + t2 = 0 + -520.7700101 -102.3302938t + t2 = 0 + -520.7700101 Combine like terms: 0 + -520.7700101 = -520.7700101 -102.3302938t + t2 = -520.7700101 The t term is -102.3302938t. Take half its coefficient (-51.1651469). Square it (2617.872257) and add it to both sides. Add '2617.872257' to each side of the equation. -102.3302938t + 2617.872257 + t2 = -520.7700101 + 2617.872257 Reorder the terms: 2617.872257 + -102.3302938t + t2 = -520.7700101 + 2617.872257 Combine like terms: -520.7700101 + 2617.872257 = 2097.1022469 2617.872257 + -102.3302938t + t2 = 2097.1022469 Factor a perfect square on the left side: (t + -51.1651469)(t + -51.1651469) = 2097.1022469 Calculate the square root of the right side: 45.794128957 Break this problem into two subproblems by setting (t + -51.1651469) equal to 45.794128957 and -45.794128957.Subproblem 1
t + -51.1651469 = 45.794128957 Simplifying t + -51.1651469 = 45.794128957 Reorder the terms: -51.1651469 + t = 45.794128957 Solving -51.1651469 + t = 45.794128957 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '51.1651469' to each side of the equation. -51.1651469 + 51.1651469 + t = 45.794128957 + 51.1651469 Combine like terms: -51.1651469 + 51.1651469 = 0.0000000 0.0000000 + t = 45.794128957 + 51.1651469 t = 45.794128957 + 51.1651469 Combine like terms: 45.794128957 + 51.1651469 = 96.959275857 t = 96.959275857 Simplifying t = 96.959275857Subproblem 2
t + -51.1651469 = -45.794128957 Simplifying t + -51.1651469 = -45.794128957 Reorder the terms: -51.1651469 + t = -45.794128957 Solving -51.1651469 + t = -45.794128957 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '51.1651469' to each side of the equation. -51.1651469 + 51.1651469 + t = -45.794128957 + 51.1651469 Combine like terms: -51.1651469 + 51.1651469 = 0.0000000 0.0000000 + t = -45.794128957 + 51.1651469 t = -45.794128957 + 51.1651469 Combine like terms: -45.794128957 + 51.1651469 = 5.371017943 t = 5.371017943 Simplifying t = 5.371017943Solution
The solution to the problem is based on the solutions from the subproblems. t = {96.959275857, 5.371017943}
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