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Simplifying 0.0001185t2 + -0.0101t + 0.0682 = 0 Reorder the terms: 0.0682 + -0.0101t + 0.0001185t2 = 0 Solving 0.0682 + -0.0101t + 0.0001185t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.0001185 the coefficient of the squared term: Divide each side by '0.0001185'. 575.5274262 + -85.23206751t + t2 = 0 Move the constant term to the right: Add '-575.5274262' to each side of the equation. 575.5274262 + -85.23206751t + -575.5274262 + t2 = 0 + -575.5274262 Reorder the terms: 575.5274262 + -575.5274262 + -85.23206751t + t2 = 0 + -575.5274262 Combine like terms: 575.5274262 + -575.5274262 = 0.0000000 0.0000000 + -85.23206751t + t2 = 0 + -575.5274262 -85.23206751t + t2 = 0 + -575.5274262 Combine like terms: 0 + -575.5274262 = -575.5274262 -85.23206751t + t2 = -575.5274262 The t term is -85.23206751t. Take half its coefficient (-42.61603376). Square it (1816.126333) and add it to both sides. Add '1816.126333' to each side of the equation. -85.23206751t + 1816.126333 + t2 = -575.5274262 + 1816.126333 Reorder the terms: 1816.126333 + -85.23206751t + t2 = -575.5274262 + 1816.126333 Combine like terms: -575.5274262 + 1816.126333 = 1240.5989068 1816.126333 + -85.23206751t + t2 = 1240.5989068 Factor a perfect square on the left side: (t + -42.61603376)(t + -42.61603376) = 1240.5989068 Calculate the square root of the right side: 35.222136602 Break this problem into two subproblems by setting (t + -42.61603376) equal to 35.222136602 and -35.222136602.Subproblem 1
t + -42.61603376 = 35.222136602 Simplifying t + -42.61603376 = 35.222136602 Reorder the terms: -42.61603376 + t = 35.222136602 Solving -42.61603376 + t = 35.222136602 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '42.61603376' to each side of the equation. -42.61603376 + 42.61603376 + t = 35.222136602 + 42.61603376 Combine like terms: -42.61603376 + 42.61603376 = 0.00000000 0.00000000 + t = 35.222136602 + 42.61603376 t = 35.222136602 + 42.61603376 Combine like terms: 35.222136602 + 42.61603376 = 77.838170362 t = 77.838170362 Simplifying t = 77.838170362Subproblem 2
t + -42.61603376 = -35.222136602 Simplifying t + -42.61603376 = -35.222136602 Reorder the terms: -42.61603376 + t = -35.222136602 Solving -42.61603376 + t = -35.222136602 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '42.61603376' to each side of the equation. -42.61603376 + 42.61603376 + t = -35.222136602 + 42.61603376 Combine like terms: -42.61603376 + 42.61603376 = 0.00000000 0.00000000 + t = -35.222136602 + 42.61603376 t = -35.222136602 + 42.61603376 Combine like terms: -35.222136602 + 42.61603376 = 7.393897158 t = 7.393897158 Simplifying t = 7.393897158Solution
The solution to the problem is based on the solutions from the subproblems. t = {77.838170362, 7.393897158}
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