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Simplifying 4.9t2 + -23t + 11 = 0 Reorder the terms: 11 + -23t + 4.9t2 = 0 Solving 11 + -23t + 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'. 2.244897959 + -4.693877551t + t2 = 0 Move the constant term to the right: Add '-2.244897959' to each side of the equation. 2.244897959 + -4.693877551t + -2.244897959 + t2 = 0 + -2.244897959 Reorder the terms: 2.244897959 + -2.244897959 + -4.693877551t + t2 = 0 + -2.244897959 Combine like terms: 2.244897959 + -2.244897959 = 0.000000000 0.000000000 + -4.693877551t + t2 = 0 + -2.244897959 -4.693877551t + t2 = 0 + -2.244897959 Combine like terms: 0 + -2.244897959 = -2.244897959 -4.693877551t + t2 = -2.244897959 The t term is -4.693877551t. Take half its coefficient (-2.346938776). Square it (5.508121618) and add it to both sides. Add '5.508121618' to each side of the equation. -4.693877551t + 5.508121618 + t2 = -2.244897959 + 5.508121618 Reorder the terms: 5.508121618 + -4.693877551t + t2 = -2.244897959 + 5.508121618 Combine like terms: -2.244897959 + 5.508121618 = 3.263223659 5.508121618 + -4.693877551t + t2 = 3.263223659 Factor a perfect square on the left side: (t + -2.346938776)(t + -2.346938776) = 3.263223659 Calculate the square root of the right side: 1.806439498 Break this problem into two subproblems by setting (t + -2.346938776) equal to 1.806439498 and -1.806439498.Subproblem 1
t + -2.346938776 = 1.806439498 Simplifying t + -2.346938776 = 1.806439498 Reorder the terms: -2.346938776 + t = 1.806439498 Solving -2.346938776 + t = 1.806439498 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.346938776' to each side of the equation. -2.346938776 + 2.346938776 + t = 1.806439498 + 2.346938776 Combine like terms: -2.346938776 + 2.346938776 = 0.000000000 0.000000000 + t = 1.806439498 + 2.346938776 t = 1.806439498 + 2.346938776 Combine like terms: 1.806439498 + 2.346938776 = 4.153378274 t = 4.153378274 Simplifying t = 4.153378274Subproblem 2
t + -2.346938776 = -1.806439498 Simplifying t + -2.346938776 = -1.806439498 Reorder the terms: -2.346938776 + t = -1.806439498 Solving -2.346938776 + t = -1.806439498 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.346938776' to each side of the equation. -2.346938776 + 2.346938776 + t = -1.806439498 + 2.346938776 Combine like terms: -2.346938776 + 2.346938776 = 0.000000000 0.000000000 + t = -1.806439498 + 2.346938776 t = -1.806439498 + 2.346938776 Combine like terms: -1.806439498 + 2.346938776 = 0.540499278 t = 0.540499278 Simplifying t = 0.540499278Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.153378274, 0.540499278}
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