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Simplifying 4.905t2 + -5t + -100 = 0 Reorder the terms: -100 + -5t + 4.905t2 = 0 Solving -100 + -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'. -20.38735984 + -1.019367992t + t2 = 0 Move the constant term to the right: Add '20.38735984' to each side of the equation. -20.38735984 + -1.019367992t + 20.38735984 + t2 = 0 + 20.38735984 Reorder the terms: -20.38735984 + 20.38735984 + -1.019367992t + t2 = 0 + 20.38735984 Combine like terms: -20.38735984 + 20.38735984 = 0.00000000 0.00000000 + -1.019367992t + t2 = 0 + 20.38735984 -1.019367992t + t2 = 0 + 20.38735984 Combine like terms: 0 + 20.38735984 = 20.38735984 -1.019367992t + t2 = 20.38735984 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 = 20.38735984 + 0.2597777758 Reorder the terms: 0.2597777758 + -1.019367992t + t2 = 20.38735984 + 0.2597777758 Combine like terms: 20.38735984 + 0.2597777758 = 20.6471376158 0.2597777758 + -1.019367992t + t2 = 20.6471376158 Factor a perfect square on the left side: (t + -0.509683996)(t + -0.509683996) = 20.6471376158 Calculate the square root of the right side: 4.543912149 Break this problem into two subproblems by setting (t + -0.509683996) equal to 4.543912149 and -4.543912149.Subproblem 1
t + -0.509683996 = 4.543912149 Simplifying t + -0.509683996 = 4.543912149 Reorder the terms: -0.509683996 + t = 4.543912149 Solving -0.509683996 + t = 4.543912149 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 = 4.543912149 + 0.509683996 Combine like terms: -0.509683996 + 0.509683996 = 0.000000000 0.000000000 + t = 4.543912149 + 0.509683996 t = 4.543912149 + 0.509683996 Combine like terms: 4.543912149 + 0.509683996 = 5.053596145 t = 5.053596145 Simplifying t = 5.053596145Subproblem 2
t + -0.509683996 = -4.543912149 Simplifying t + -0.509683996 = -4.543912149 Reorder the terms: -0.509683996 + t = -4.543912149 Solving -0.509683996 + t = -4.543912149 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 = -4.543912149 + 0.509683996 Combine like terms: -0.509683996 + 0.509683996 = 0.000000000 0.000000000 + t = -4.543912149 + 0.509683996 t = -4.543912149 + 0.509683996 Combine like terms: -4.543912149 + 0.509683996 = -4.034228153 t = -4.034228153 Simplifying t = -4.034228153Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.053596145, -4.034228153}
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