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Simplifying (4.905t2) + -1(16t) + 3 = 0 Remove parenthesis around (16t) (4.905t2) + -1 * 16t + 3 = 0 Multiply -1 * 16 (4.905t2) + -16t + 3 = 0 Reorder the terms: 3 + -16t + (4.905t2) = 0 Solving 3 + -16t + (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'. 0.6116207951 + -3.261977574t + t2 = 0 Move the constant term to the right: Add '-0.6116207951' to each side of the equation. 0.6116207951 + -3.261977574t + -0.6116207951 + t2 = 0 + -0.6116207951 Reorder the terms: 0.6116207951 + -0.6116207951 + -3.261977574t + t2 = 0 + -0.6116207951 Combine like terms: 0.6116207951 + -0.6116207951 = 0.0000000000 0.0000000000 + -3.261977574t + t2 = 0 + -0.6116207951 -3.261977574t + t2 = 0 + -0.6116207951 Combine like terms: 0 + -0.6116207951 = -0.6116207951 -3.261977574t + t2 = -0.6116207951 The t term is -3.261977574t. Take half its coefficient (-1.630988787). Square it (2.660124423) and add it to both sides. Add '2.660124423' to each side of the equation. -3.261977574t + 2.660124423 + t2 = -0.6116207951 + 2.660124423 Reorder the terms: 2.660124423 + -3.261977574t + t2 = -0.6116207951 + 2.660124423 Combine like terms: -0.6116207951 + 2.660124423 = 2.0485036279 2.660124423 + -3.261977574t + t2 = 2.0485036279 Factor a perfect square on the left side: ((t) + -1.630988787)((t) + -1.630988787) = 2.0485036279 Calculate the square root of the right side: 1.431259455 Break this problem into two subproblems by setting ((t) + -1.630988787) equal to 1.431259455 and -1.431259455.Subproblem 1
(t) + -1.630988787 = 1.431259455 Simplifying (t) + -1.630988787 = 1.431259455 t + -1.630988787 = 1.431259455 Reorder the terms: -1.630988787 + t = 1.431259455 Solving -1.630988787 + t = 1.431259455 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.630988787' to each side of the equation. -1.630988787 + 1.630988787 + t = 1.431259455 + 1.630988787 Combine like terms: -1.630988787 + 1.630988787 = 0.000000000 0.000000000 + t = 1.431259455 + 1.630988787 t = 1.431259455 + 1.630988787 Combine like terms: 1.431259455 + 1.630988787 = 3.062248242 t = 3.062248242 Simplifying t = 3.062248242Subproblem 2
(t) + -1.630988787 = -1.431259455 Simplifying (t) + -1.630988787 = -1.431259455 t + -1.630988787 = -1.431259455 Reorder the terms: -1.630988787 + t = -1.431259455 Solving -1.630988787 + t = -1.431259455 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.630988787' to each side of the equation. -1.630988787 + 1.630988787 + t = -1.431259455 + 1.630988787 Combine like terms: -1.630988787 + 1.630988787 = 0.000000000 0.000000000 + t = -1.431259455 + 1.630988787 t = -1.431259455 + 1.630988787 Combine like terms: -1.431259455 + 1.630988787 = 0.199729332 t = 0.199729332 Simplifying t = 0.199729332Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.062248242, 0.199729332}
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