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Simplifying -4.9t2 + 23t + 5 = 0 Reorder the terms: 5 + 23t + -4.9t2 = 0 Solving 5 + 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'. -1.020408163 + -4.693877551t + t2 = 0 Move the constant term to the right: Add '1.020408163' to each side of the equation. -1.020408163 + -4.693877551t + 1.020408163 + t2 = 0 + 1.020408163 Reorder the terms: -1.020408163 + 1.020408163 + -4.693877551t + t2 = 0 + 1.020408163 Combine like terms: -1.020408163 + 1.020408163 = 0.000000000 0.000000000 + -4.693877551t + t2 = 0 + 1.020408163 -4.693877551t + t2 = 0 + 1.020408163 Combine like terms: 0 + 1.020408163 = 1.020408163 -4.693877551t + t2 = 1.020408163 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 = 1.020408163 + 5.508121618 Reorder the terms: 5.508121618 + -4.693877551t + t2 = 1.020408163 + 5.508121618 Combine like terms: 1.020408163 + 5.508121618 = 6.528529781 5.508121618 + -4.693877551t + t2 = 6.528529781 Factor a perfect square on the left side: (t + -2.346938776)(t + -2.346938776) = 6.528529781 Calculate the square root of the right side: 2.555098781 Break this problem into two subproblems by setting (t + -2.346938776) equal to 2.555098781 and -2.555098781.Subproblem 1
t + -2.346938776 = 2.555098781 Simplifying t + -2.346938776 = 2.555098781 Reorder the terms: -2.346938776 + t = 2.555098781 Solving -2.346938776 + t = 2.555098781 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 = 2.555098781 + 2.346938776 Combine like terms: -2.346938776 + 2.346938776 = 0.000000000 0.000000000 + t = 2.555098781 + 2.346938776 t = 2.555098781 + 2.346938776 Combine like terms: 2.555098781 + 2.346938776 = 4.902037557 t = 4.902037557 Simplifying t = 4.902037557Subproblem 2
t + -2.346938776 = -2.555098781 Simplifying t + -2.346938776 = -2.555098781 Reorder the terms: -2.346938776 + t = -2.555098781 Solving -2.346938776 + t = -2.555098781 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 = -2.555098781 + 2.346938776 Combine like terms: -2.346938776 + 2.346938776 = 0.000000000 0.000000000 + t = -2.555098781 + 2.346938776 t = -2.555098781 + 2.346938776 Combine like terms: -2.555098781 + 2.346938776 = -0.208160005 t = -0.208160005 Simplifying t = -0.208160005Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.902037557, -0.208160005}
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