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Simplifying 4.9t2 + 18t + -10 = 0 Reorder the terms: -10 + 18t + 4.9t2 = 0 Solving -10 + 18t + 4.9t2 = 0 Solving for variable 't'. 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 = 5.414410663 3.373594336 + 3.673469388t + t2 = 5.414410663 Factor a perfect square on the left side: (t + 1.836734694)(t + 1.836734694) = 5.414410663 Calculate the square root of the right side: 2.326888623 Break this problem into two subproblems by setting (t + 1.836734694) equal to 2.326888623 and -2.326888623.Subproblem 1
t + 1.836734694 = 2.326888623 Simplifying t + 1.836734694 = 2.326888623 Reorder the terms: 1.836734694 + t = 2.326888623 Solving 1.836734694 + t = 2.326888623 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 = 2.326888623 + -1.836734694 Combine like terms: 1.836734694 + -1.836734694 = 0.000000000 0.000000000 + t = 2.326888623 + -1.836734694 t = 2.326888623 + -1.836734694 Combine like terms: 2.326888623 + -1.836734694 = 0.490153929 t = 0.490153929 Simplifying t = 0.490153929Subproblem 2
t + 1.836734694 = -2.326888623 Simplifying t + 1.836734694 = -2.326888623 Reorder the terms: 1.836734694 + t = -2.326888623 Solving 1.836734694 + t = -2.326888623 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 = -2.326888623 + -1.836734694 Combine like terms: 1.836734694 + -1.836734694 = 0.000000000 0.000000000 + t = -2.326888623 + -1.836734694 t = -2.326888623 + -1.836734694 Combine like terms: -2.326888623 + -1.836734694 = -4.163623317 t = -4.163623317 Simplifying t = -4.163623317Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.490153929, -4.163623317}
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