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Simplifying -10 = 4t + (-4.905) * t2 Solving -10 = 4t + -4.905t2 Solving for variable 't'. Reorder the terms: -10 + -4t + 4.905t2 = 4t + -4t + -4.905t2 + 4.905t2 Combine like terms: 4t + -4t = 0 -10 + -4t + 4.905t2 = 0 + -4.905t2 + 4.905t2 -10 + -4t + 4.905t2 = -4.905t2 + 4.905t2 Combine like terms: -4.905t2 + 4.905t2 = 0.000 -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'. -2.038735984 + -0.8154943935t + t2 = 0 Move the constant term to the right: Add '2.038735984' to each side of the equation. -2.038735984 + -0.8154943935t + 2.038735984 + t2 = 0 + 2.038735984 Reorder the terms: -2.038735984 + 2.038735984 + -0.8154943935t + t2 = 0 + 2.038735984 Combine like terms: -2.038735984 + 2.038735984 = 0.000000000 0.000000000 + -0.8154943935t + t2 = 0 + 2.038735984 -0.8154943935t + t2 = 0 + 2.038735984 Combine like terms: 0 + 2.038735984 = 2.038735984 -0.8154943935t + t2 = 2.038735984 The t term is -0.8154943935t. Take half its coefficient (-0.4077471968). Square it (0.1662577765) and add it to both sides. Add '0.1662577765' to each side of the equation. -0.8154943935t + 0.1662577765 + t2 = 2.038735984 + 0.1662577765 Reorder the terms: 0.1662577765 + -0.8154943935t + t2 = 2.038735984 + 0.1662577765 Combine like terms: 2.038735984 + 0.1662577765 = 2.2049937605 0.1662577765 + -0.8154943935t + t2 = 2.2049937605 Factor a perfect square on the left side: (t + -0.4077471968)(t + -0.4077471968) = 2.2049937605 Calculate the square root of the right side: 1.48492214 Break this problem into two subproblems by setting (t + -0.4077471968) equal to 1.48492214 and -1.48492214.Subproblem 1
t + -0.4077471968 = 1.48492214 Simplifying t + -0.4077471968 = 1.48492214 Reorder the terms: -0.4077471968 + t = 1.48492214 Solving -0.4077471968 + t = 1.48492214 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4077471968' to each side of the equation. -0.4077471968 + 0.4077471968 + t = 1.48492214 + 0.4077471968 Combine like terms: -0.4077471968 + 0.4077471968 = 0.0000000000 0.0000000000 + t = 1.48492214 + 0.4077471968 t = 1.48492214 + 0.4077471968 Combine like terms: 1.48492214 + 0.4077471968 = 1.8926693368 t = 1.8926693368 Simplifying t = 1.8926693368Subproblem 2
t + -0.4077471968 = -1.48492214 Simplifying t + -0.4077471968 = -1.48492214 Reorder the terms: -0.4077471968 + t = -1.48492214 Solving -0.4077471968 + t = -1.48492214 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4077471968' to each side of the equation. -0.4077471968 + 0.4077471968 + t = -1.48492214 + 0.4077471968 Combine like terms: -0.4077471968 + 0.4077471968 = 0.0000000000 0.0000000000 + t = -1.48492214 + 0.4077471968 t = -1.48492214 + 0.4077471968 Combine like terms: -1.48492214 + 0.4077471968 = -1.0771749432 t = -1.0771749432 Simplifying t = -1.0771749432Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.8926693368, -1.0771749432}
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