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Simplifying 4.9t2 + -23t + -10 = 0 Reorder the terms: -10 + -23t + 4.9t2 = 0 Solving -10 + -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'. -2.040816327 + -4.693877551t + t2 = 0 Move the constant term to the right: Add '2.040816327' to each side of the equation. -2.040816327 + -4.693877551t + 2.040816327 + t2 = 0 + 2.040816327 Reorder the terms: -2.040816327 + 2.040816327 + -4.693877551t + t2 = 0 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + -4.693877551t + t2 = 0 + 2.040816327 -4.693877551t + t2 = 0 + 2.040816327 Combine like terms: 0 + 2.040816327 = 2.040816327 -4.693877551t + t2 = 2.040816327 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 = 2.040816327 + 5.508121618 Reorder the terms: 5.508121618 + -4.693877551t + t2 = 2.040816327 + 5.508121618 Combine like terms: 2.040816327 + 5.508121618 = 7.548937945 5.508121618 + -4.693877551t + t2 = 7.548937945 Factor a perfect square on the left side: (t + -2.346938776)(t + -2.346938776) = 7.548937945 Calculate the square root of the right side: 2.747533065 Break this problem into two subproblems by setting (t + -2.346938776) equal to 2.747533065 and -2.747533065.Subproblem 1
t + -2.346938776 = 2.747533065 Simplifying t + -2.346938776 = 2.747533065 Reorder the terms: -2.346938776 + t = 2.747533065 Solving -2.346938776 + t = 2.747533065 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 = 2.747533065 + 2.346938776 Combine like terms: -2.346938776 + 2.346938776 = 0.000000000 0.000000000 + t = 2.747533065 + 2.346938776 t = 2.747533065 + 2.346938776 Combine like terms: 2.747533065 + 2.346938776 = 5.094471841 t = 5.094471841 Simplifying t = 5.094471841Subproblem 2
t + -2.346938776 = -2.747533065 Simplifying t + -2.346938776 = -2.747533065 Reorder the terms: -2.346938776 + t = -2.747533065 Solving -2.346938776 + t = -2.747533065 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 = -2.747533065 + 2.346938776 Combine like terms: -2.346938776 + 2.346938776 = 0.000000000 0.000000000 + t = -2.747533065 + 2.346938776 t = -2.747533065 + 2.346938776 Combine like terms: -2.747533065 + 2.346938776 = -0.400594289 t = -0.400594289 Simplifying t = -0.400594289Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.094471841, -0.400594289}
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