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Simplifying -4.905t2 + 12t + 25 = 0 Reorder the terms: 25 + 12t + -4.905t2 = 0 Solving 25 + 12t + -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'. -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 = 3.790956517 t = 3.790956517 Simplifying t = 3.790956517Subproblem 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 = -1.344473337 t = -1.344473337 Simplifying t = -1.344473337Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.790956517, -1.344473337}
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