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Simplifying -25 = -12t + -0.5(9.81) * t2 Multiply -0.5 * 9.81 -25 = -12t + -4.905t2 Solving -25 = -12t + -4.905t2 Solving for variable 't'. Reorder the terms: -25 + 12t + 4.905t2 = -12t + 12t + -4.905t2 + 4.905t2 Combine like terms: -12t + 12t = 0 -25 + 12t + 4.905t2 = 0 + -4.905t2 + 4.905t2 -25 + 12t + 4.905t2 = -4.905t2 + 4.905t2 Combine like terms: -4.905t2 + 4.905t2 = 0.000 -25 + 12t + 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'. -5.096839959 + 2.44648318t + t2 = 0 Move the constant term to the right: Add '5.096839959' to each side of the equation. -5.096839959 + 2.44648318t + 5.096839959 + t2 = 0 + 5.096839959 Reorder the terms: -5.096839959 + 5.096839959 + 2.44648318t + t2 = 0 + 5.096839959 Combine like terms: -5.096839959 + 5.096839959 = 0.000000000 0.000000000 + 2.44648318t + t2 = 0 + 5.096839959 2.44648318t + t2 = 0 + 5.096839959 Combine like terms: 0 + 5.096839959 = 5.096839959 2.44648318t + t2 = 5.096839959 The t term is 2.44648318t. Take half its coefficient (1.22324159). Square it (1.496319988) and add it to both sides. Add '1.496319988' to each side of the equation. 2.44648318t + 1.496319988 + t2 = 5.096839959 + 1.496319988 Reorder the terms: 1.496319988 + 2.44648318t + t2 = 5.096839959 + 1.496319988 Combine like terms: 5.096839959 + 1.496319988 = 6.593159947 1.496319988 + 2.44648318t + t2 = 6.593159947 Factor a perfect square on the left side: (t + 1.22324159)(t + 1.22324159) = 6.593159947 Calculate the square root of the right side: 2.567714927 Break this problem into two subproblems by setting (t + 1.22324159) equal to 2.567714927 and -2.567714927.Subproblem 1
t + 1.22324159 = 2.567714927 Simplifying t + 1.22324159 = 2.567714927 Reorder the terms: 1.22324159 + t = 2.567714927 Solving 1.22324159 + t = 2.567714927 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.22324159' to each side of the equation. 1.22324159 + -1.22324159 + t = 2.567714927 + -1.22324159 Combine like terms: 1.22324159 + -1.22324159 = 0.00000000 0.00000000 + t = 2.567714927 + -1.22324159 t = 2.567714927 + -1.22324159 Combine like terms: 2.567714927 + -1.22324159 = 1.344473337 t = 1.344473337 Simplifying t = 1.344473337Subproblem 2
t + 1.22324159 = -2.567714927 Simplifying t + 1.22324159 = -2.567714927 Reorder the terms: 1.22324159 + t = -2.567714927 Solving 1.22324159 + t = -2.567714927 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.22324159' to each side of the equation. 1.22324159 + -1.22324159 + t = -2.567714927 + -1.22324159 Combine like terms: 1.22324159 + -1.22324159 = 0.00000000 0.00000000 + t = -2.567714927 + -1.22324159 t = -2.567714927 + -1.22324159 Combine like terms: -2.567714927 + -1.22324159 = -3.790956517 t = -3.790956517 Simplifying t = -3.790956517Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.344473337, -3.790956517}
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