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Simplifying 4.905t2 + 5t + -16 = 0 Reorder the terms: -16 + 5t + 4.905t2 = 0 Solving -16 + 5t + 4.905t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4.905 the coefficient of the squared term: Divide each side by '4.905'. -3.261977574 + 1.019367992t + t2 = 0 Move the constant term to the right: Add '3.261977574' to each side of the equation. -3.261977574 + 1.019367992t + 3.261977574 + t2 = 0 + 3.261977574 Reorder the terms: -3.261977574 + 3.261977574 + 1.019367992t + t2 = 0 + 3.261977574 Combine like terms: -3.261977574 + 3.261977574 = 0.000000000 0.000000000 + 1.019367992t + t2 = 0 + 3.261977574 1.019367992t + t2 = 0 + 3.261977574 Combine like terms: 0 + 3.261977574 = 3.261977574 1.019367992t + t2 = 3.261977574 The t term is 1.019367992t. Take half its coefficient (0.509683996). Square it (0.2597777758) and add it to both sides. Add '0.2597777758' to each side of the equation. 1.019367992t + 0.2597777758 + t2 = 3.261977574 + 0.2597777758 Reorder the terms: 0.2597777758 + 1.019367992t + t2 = 3.261977574 + 0.2597777758 Combine like terms: 3.261977574 + 0.2597777758 = 3.5217553498 0.2597777758 + 1.019367992t + t2 = 3.5217553498 Factor a perfect square on the left side: (t + 0.509683996)(t + 0.509683996) = 3.5217553498 Calculate the square root of the right side: 1.876634048 Break this problem into two subproblems by setting (t + 0.509683996) equal to 1.876634048 and -1.876634048.Subproblem 1
t + 0.509683996 = 1.876634048 Simplifying t + 0.509683996 = 1.876634048 Reorder the terms: 0.509683996 + t = 1.876634048 Solving 0.509683996 + t = 1.876634048 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.509683996' to each side of the equation. 0.509683996 + -0.509683996 + t = 1.876634048 + -0.509683996 Combine like terms: 0.509683996 + -0.509683996 = 0.000000000 0.000000000 + t = 1.876634048 + -0.509683996 t = 1.876634048 + -0.509683996 Combine like terms: 1.876634048 + -0.509683996 = 1.366950052 t = 1.366950052 Simplifying t = 1.366950052Subproblem 2
t + 0.509683996 = -1.876634048 Simplifying t + 0.509683996 = -1.876634048 Reorder the terms: 0.509683996 + t = -1.876634048 Solving 0.509683996 + t = -1.876634048 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.509683996' to each side of the equation. 0.509683996 + -0.509683996 + t = -1.876634048 + -0.509683996 Combine like terms: 0.509683996 + -0.509683996 = 0.000000000 0.000000000 + t = -1.876634048 + -0.509683996 t = -1.876634048 + -0.509683996 Combine like terms: -1.876634048 + -0.509683996 = -2.386318044 t = -2.386318044 Simplifying t = -2.386318044Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.366950052, -2.386318044}
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