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Simplifying 40 * 3.14 + -1.5t + 0.00224t2 = 0 Multiply 40 * 3.14 125.6 + -1.5t + 0.00224t2 = 0 Solving 125.6 + -1.5t + 0.00224t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.00224 the coefficient of the squared term: Divide each side by '0.00224'. 56071.42857 + -669.6428571t + t2 = 0 Move the constant term to the right: Add '-56071.42857' to each side of the equation. 56071.42857 + -669.6428571t + -56071.42857 + t2 = 0 + -56071.42857 Reorder the terms: 56071.42857 + -56071.42857 + -669.6428571t + t2 = 0 + -56071.42857 Combine like terms: 56071.42857 + -56071.42857 = 0.00000 0.00000 + -669.6428571t + t2 = 0 + -56071.42857 -669.6428571t + t2 = 0 + -56071.42857 Combine like terms: 0 + -56071.42857 = -56071.42857 -669.6428571t + t2 = -56071.42857 The t term is -669.6428571t. Take half its coefficient (-334.8214286). Square it (112105.3891) and add it to both sides. Add '112105.3891' to each side of the equation. -669.6428571t + 112105.3891 + t2 = -56071.42857 + 112105.3891 Reorder the terms: 112105.3891 + -669.6428571t + t2 = -56071.42857 + 112105.3891 Combine like terms: -56071.42857 + 112105.3891 = 56033.96053 112105.3891 + -669.6428571t + t2 = 56033.96053 Factor a perfect square on the left side: (t + -334.8214286)(t + -334.8214286) = 56033.96053 Calculate the square root of the right side: 236.714935165 Break this problem into two subproblems by setting (t + -334.8214286) equal to 236.714935165 and -236.714935165.Subproblem 1
t + -334.8214286 = 236.714935165 Simplifying t + -334.8214286 = 236.714935165 Reorder the terms: -334.8214286 + t = 236.714935165 Solving -334.8214286 + t = 236.714935165 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '334.8214286' to each side of the equation. -334.8214286 + 334.8214286 + t = 236.714935165 + 334.8214286 Combine like terms: -334.8214286 + 334.8214286 = 0.0000000 0.0000000 + t = 236.714935165 + 334.8214286 t = 236.714935165 + 334.8214286 Combine like terms: 236.714935165 + 334.8214286 = 571.536363765 t = 571.536363765 Simplifying t = 571.536363765Subproblem 2
t + -334.8214286 = -236.714935165 Simplifying t + -334.8214286 = -236.714935165 Reorder the terms: -334.8214286 + t = -236.714935165 Solving -334.8214286 + t = -236.714935165 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '334.8214286' to each side of the equation. -334.8214286 + 334.8214286 + t = -236.714935165 + 334.8214286 Combine like terms: -334.8214286 + 334.8214286 = 0.0000000 0.0000000 + t = -236.714935165 + 334.8214286 t = -236.714935165 + 334.8214286 Combine like terms: -236.714935165 + 334.8214286 = 98.106493435 t = 98.106493435 Simplifying t = 98.106493435Solution
The solution to the problem is based on the solutions from the subproblems. t = {571.536363765, 98.106493435}
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