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Simplifying 4.9t2 + -4.704t + -0.25 = 0 Reorder the terms: -0.25 + -4.704t + 4.9t2 = 0 Solving -0.25 + -4.704t + 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'. -0.05102040816 + -0.96t + t2 = 0 Move the constant term to the right: Add '0.05102040816' to each side of the equation. -0.05102040816 + -0.96t + 0.05102040816 + t2 = 0 + 0.05102040816 Reorder the terms: -0.05102040816 + 0.05102040816 + -0.96t + t2 = 0 + 0.05102040816 Combine like terms: -0.05102040816 + 0.05102040816 = 0.00000000000 0.00000000000 + -0.96t + t2 = 0 + 0.05102040816 -0.96t + t2 = 0 + 0.05102040816 Combine like terms: 0 + 0.05102040816 = 0.05102040816 -0.96t + t2 = 0.05102040816 The t term is -0.96t. Take half its coefficient (-0.48). Square it (0.2304) and add it to both sides. Add '0.2304' to each side of the equation. -0.96t + 0.2304 + t2 = 0.05102040816 + 0.2304 Reorder the terms: 0.2304 + -0.96t + t2 = 0.05102040816 + 0.2304 Combine like terms: 0.05102040816 + 0.2304 = 0.28142040816 0.2304 + -0.96t + t2 = 0.28142040816 Factor a perfect square on the left side: (t + -0.48)(t + -0.48) = 0.28142040816 Calculate the square root of the right side: 0.530490724 Break this problem into two subproblems by setting (t + -0.48) equal to 0.530490724 and -0.530490724.Subproblem 1
t + -0.48 = 0.530490724 Simplifying t + -0.48 = 0.530490724 Reorder the terms: -0.48 + t = 0.530490724 Solving -0.48 + t = 0.530490724 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.48' to each side of the equation. -0.48 + 0.48 + t = 0.530490724 + 0.48 Combine like terms: -0.48 + 0.48 = 0.00 0.00 + t = 0.530490724 + 0.48 t = 0.530490724 + 0.48 Combine like terms: 0.530490724 + 0.48 = 1.010490724 t = 1.010490724 Simplifying t = 1.010490724Subproblem 2
t + -0.48 = -0.530490724 Simplifying t + -0.48 = -0.530490724 Reorder the terms: -0.48 + t = -0.530490724 Solving -0.48 + t = -0.530490724 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.48' to each side of the equation. -0.48 + 0.48 + t = -0.530490724 + 0.48 Combine like terms: -0.48 + 0.48 = 0.00 0.00 + t = -0.530490724 + 0.48 t = -0.530490724 + 0.48 Combine like terms: -0.530490724 + 0.48 = -0.050490724 t = -0.050490724 Simplifying t = -0.050490724Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.010490724, -0.050490724}
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