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Simplifying -4.9t2 + 18t = 10 Reorder the terms: 18t + -4.9t2 = 10 Solving 18t + -4.9t2 = 10 Solving for variable 't'. Reorder the terms: -10 + 18t + -4.9t2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 18t + -4.9t2 = 0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. 2.040816327 + -3.673469388t + t2 = 0 Move the constant term to the right: Add '-2.040816327' to each side of the equation. 2.040816327 + -3.673469388t + -2.040816327 + t2 = 0 + -2.040816327 Reorder the terms: 2.040816327 + -2.040816327 + -3.673469388t + t2 = 0 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + -3.673469388t + t2 = 0 + -2.040816327 -3.673469388t + t2 = 0 + -2.040816327 Combine like terms: 0 + -2.040816327 = -2.040816327 -3.673469388t + t2 = -2.040816327 The t term is -3.673469388t. Take half its coefficient (-1.836734694). Square it (3.373594336) and add it to both sides. Add '3.373594336' to each side of the equation. -3.673469388t + 3.373594336 + t2 = -2.040816327 + 3.373594336 Reorder the terms: 3.373594336 + -3.673469388t + t2 = -2.040816327 + 3.373594336 Combine like terms: -2.040816327 + 3.373594336 = 1.332778009 3.373594336 + -3.673469388t + t2 = 1.332778009 Factor a perfect square on the left side: (t + -1.836734694)(t + -1.836734694) = 1.332778009 Calculate the square root of the right side: 1.154460051 Break this problem into two subproblems by setting (t + -1.836734694) equal to 1.154460051 and -1.154460051.Subproblem 1
t + -1.836734694 = 1.154460051 Simplifying t + -1.836734694 = 1.154460051 Reorder the terms: -1.836734694 + t = 1.154460051 Solving -1.836734694 + t = 1.154460051 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.836734694' to each side of the equation. -1.836734694 + 1.836734694 + t = 1.154460051 + 1.836734694 Combine like terms: -1.836734694 + 1.836734694 = 0.000000000 0.000000000 + t = 1.154460051 + 1.836734694 t = 1.154460051 + 1.836734694 Combine like terms: 1.154460051 + 1.836734694 = 2.991194745 t = 2.991194745 Simplifying t = 2.991194745Subproblem 2
t + -1.836734694 = -1.154460051 Simplifying t + -1.836734694 = -1.154460051 Reorder the terms: -1.836734694 + t = -1.154460051 Solving -1.836734694 + t = -1.154460051 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.836734694' to each side of the equation. -1.836734694 + 1.836734694 + t = -1.154460051 + 1.836734694 Combine like terms: -1.836734694 + 1.836734694 = 0.000000000 0.000000000 + t = -1.154460051 + 1.836734694 t = -1.154460051 + 1.836734694 Combine like terms: -1.154460051 + 1.836734694 = 0.682274643 t = 0.682274643 Simplifying t = 0.682274643Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.991194745, 0.682274643}
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