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Simplifying 4.905t2 + -5t + 0.65 = 0 Reorder the terms: 0.65 + -5t + 4.905t2 = 0 Solving 0.65 + -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'. 0.1325178389 + -1.019367992t + t2 = 0 Move the constant term to the right: Add '-0.1325178389' to each side of the equation. 0.1325178389 + -1.019367992t + -0.1325178389 + t2 = 0 + -0.1325178389 Reorder the terms: 0.1325178389 + -0.1325178389 + -1.019367992t + t2 = 0 + -0.1325178389 Combine like terms: 0.1325178389 + -0.1325178389 = 0.0000000000 0.0000000000 + -1.019367992t + t2 = 0 + -0.1325178389 -1.019367992t + t2 = 0 + -0.1325178389 Combine like terms: 0 + -0.1325178389 = -0.1325178389 -1.019367992t + t2 = -0.1325178389 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 = -0.1325178389 + 0.2597777758 Reorder the terms: 0.2597777758 + -1.019367992t + t2 = -0.1325178389 + 0.2597777758 Combine like terms: -0.1325178389 + 0.2597777758 = 0.1272599369 0.2597777758 + -1.019367992t + t2 = 0.1272599369 Factor a perfect square on the left side: (t + -0.509683996)(t + -0.509683996) = 0.1272599369 Calculate the square root of the right side: 0.356735107 Break this problem into two subproblems by setting (t + -0.509683996) equal to 0.356735107 and -0.356735107.Subproblem 1
t + -0.509683996 = 0.356735107 Simplifying t + -0.509683996 = 0.356735107 Reorder the terms: -0.509683996 + t = 0.356735107 Solving -0.509683996 + t = 0.356735107 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 = 0.356735107 + 0.509683996 Combine like terms: -0.509683996 + 0.509683996 = 0.000000000 0.000000000 + t = 0.356735107 + 0.509683996 t = 0.356735107 + 0.509683996 Combine like terms: 0.356735107 + 0.509683996 = 0.866419103 t = 0.866419103 Simplifying t = 0.866419103Subproblem 2
t + -0.509683996 = -0.356735107 Simplifying t + -0.509683996 = -0.356735107 Reorder the terms: -0.509683996 + t = -0.356735107 Solving -0.509683996 + t = -0.356735107 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 = -0.356735107 + 0.509683996 Combine like terms: -0.509683996 + 0.509683996 = 0.000000000 0.000000000 + t = -0.356735107 + 0.509683996 t = -0.356735107 + 0.509683996 Combine like terms: -0.356735107 + 0.509683996 = 0.152948889 t = 0.152948889 Simplifying t = 0.152948889Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.866419103, 0.152948889}
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