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Simplifying -21.5 = 10.4t + (-4.905) * t2 Solving -21.5 = 10.4t + -4.905t2 Solving for variable 't'. Reorder the terms: -21.5 + -10.4t + 4.905t2 = 10.4t + -10.4t + -4.905t2 + 4.905t2 Combine like terms: 10.4t + -10.4t = 0.0 -21.5 + -10.4t + 4.905t2 = 0.0 + -4.905t2 + 4.905t2 -21.5 + -10.4t + 4.905t2 = -4.905t2 + 4.905t2 Combine like terms: -4.905t2 + 4.905t2 = 0.000 -21.5 + -10.4t + 4.905t2 = 0.000 Begin completing the square. Divide all terms by 4.905 the coefficient of the squared term: Divide each side by '4.905'. -4.383282365 + -2.120285423t + t2 = 0 Move the constant term to the right: Add '4.383282365' to each side of the equation. -4.383282365 + -2.120285423t + 4.383282365 + t2 = 0 + 4.383282365 Reorder the terms: -4.383282365 + 4.383282365 + -2.120285423t + t2 = 0 + 4.383282365 Combine like terms: -4.383282365 + 4.383282365 = 0.000000000 0.000000000 + -2.120285423t + t2 = 0 + 4.383282365 -2.120285423t + t2 = 0 + 4.383282365 Combine like terms: 0 + 4.383282365 = 4.383282365 -2.120285423t + t2 = 4.383282365 The t term is -2.120285423t. Take half its coefficient (-1.060142712). Square it (1.123902570) and add it to both sides. Add '1.123902570' to each side of the equation. -2.120285423t + 1.123902570 + t2 = 4.383282365 + 1.123902570 Reorder the terms: 1.123902570 + -2.120285423t + t2 = 4.383282365 + 1.123902570 Combine like terms: 4.383282365 + 1.123902570 = 5.507184935 1.123902570 + -2.120285423t + t2 = 5.507184935 Factor a perfect square on the left side: (t + -1.060142712)(t + -1.060142712) = 5.507184935 Calculate the square root of the right side: 2.346739213 Break this problem into two subproblems by setting (t + -1.060142712) equal to 2.346739213 and -2.346739213.Subproblem 1
t + -1.060142712 = 2.346739213 Simplifying t + -1.060142712 = 2.346739213 Reorder the terms: -1.060142712 + t = 2.346739213 Solving -1.060142712 + t = 2.346739213 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.060142712' to each side of the equation. -1.060142712 + 1.060142712 + t = 2.346739213 + 1.060142712 Combine like terms: -1.060142712 + 1.060142712 = 0.000000000 0.000000000 + t = 2.346739213 + 1.060142712 t = 2.346739213 + 1.060142712 Combine like terms: 2.346739213 + 1.060142712 = 3.406881925 t = 3.406881925 Simplifying t = 3.406881925Subproblem 2
t + -1.060142712 = -2.346739213 Simplifying t + -1.060142712 = -2.346739213 Reorder the terms: -1.060142712 + t = -2.346739213 Solving -1.060142712 + t = -2.346739213 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.060142712' to each side of the equation. -1.060142712 + 1.060142712 + t = -2.346739213 + 1.060142712 Combine like terms: -1.060142712 + 1.060142712 = 0.000000000 0.000000000 + t = -2.346739213 + 1.060142712 t = -2.346739213 + 1.060142712 Combine like terms: -2.346739213 + 1.060142712 = -1.286596501 t = -1.286596501 Simplifying t = -1.286596501Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.406881925, -1.286596501}
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