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Simplifying 0.0915t2 + -0.938t + 1.705 = 0 Reorder the terms: 1.705 + -0.938t + 0.0915t2 = 0 Solving 1.705 + -0.938t + 0.0915t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.0915 the coefficient of the squared term: Divide each side by '0.0915'. 18.63387978 + -10.25136612t + t2 = 0 Move the constant term to the right: Add '-18.63387978' to each side of the equation. 18.63387978 + -10.25136612t + -18.63387978 + t2 = 0 + -18.63387978 Reorder the terms: 18.63387978 + -18.63387978 + -10.25136612t + t2 = 0 + -18.63387978 Combine like terms: 18.63387978 + -18.63387978 = 0.00000000 0.00000000 + -10.25136612t + t2 = 0 + -18.63387978 -10.25136612t + t2 = 0 + -18.63387978 Combine like terms: 0 + -18.63387978 = -18.63387978 -10.25136612t + t2 = -18.63387978 The t term is -10.25136612t. Take half its coefficient (-5.12568306). Square it (26.27262683) and add it to both sides. Add '26.27262683' to each side of the equation. -10.25136612t + 26.27262683 + t2 = -18.63387978 + 26.27262683 Reorder the terms: 26.27262683 + -10.25136612t + t2 = -18.63387978 + 26.27262683 Combine like terms: -18.63387978 + 26.27262683 = 7.63874705 26.27262683 + -10.25136612t + t2 = 7.63874705 Factor a perfect square on the left side: (t + -5.12568306)(t + -5.12568306) = 7.63874705 Calculate the square root of the right side: 2.763828332 Break this problem into two subproblems by setting (t + -5.12568306) equal to 2.763828332 and -2.763828332.Subproblem 1
t + -5.12568306 = 2.763828332 Simplifying t + -5.12568306 = 2.763828332 Reorder the terms: -5.12568306 + t = 2.763828332 Solving -5.12568306 + t = 2.763828332 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.12568306' to each side of the equation. -5.12568306 + 5.12568306 + t = 2.763828332 + 5.12568306 Combine like terms: -5.12568306 + 5.12568306 = 0.00000000 0.00000000 + t = 2.763828332 + 5.12568306 t = 2.763828332 + 5.12568306 Combine like terms: 2.763828332 + 5.12568306 = 7.889511392 t = 7.889511392 Simplifying t = 7.889511392Subproblem 2
t + -5.12568306 = -2.763828332 Simplifying t + -5.12568306 = -2.763828332 Reorder the terms: -5.12568306 + t = -2.763828332 Solving -5.12568306 + t = -2.763828332 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.12568306' to each side of the equation. -5.12568306 + 5.12568306 + t = -2.763828332 + 5.12568306 Combine like terms: -5.12568306 + 5.12568306 = 0.00000000 0.00000000 + t = -2.763828332 + 5.12568306 t = -2.763828332 + 5.12568306 Combine like terms: -2.763828332 + 5.12568306 = 2.361854728 t = 2.361854728 Simplifying t = 2.361854728Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.889511392, 2.361854728}
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