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Simplifying 4.9t2 + 23t + 6 = 0 Reorder the terms: 6 + 23t + 4.9t2 = 0 Solving 6 + 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'. 1.224489796 + 4.693877551t + t2 = 0 Move the constant term to the right: Add '-1.224489796' to each side of the equation. 1.224489796 + 4.693877551t + -1.224489796 + t2 = 0 + -1.224489796 Reorder the terms: 1.224489796 + -1.224489796 + 4.693877551t + t2 = 0 + -1.224489796 Combine like terms: 1.224489796 + -1.224489796 = 0.000000000 0.000000000 + 4.693877551t + t2 = 0 + -1.224489796 4.693877551t + t2 = 0 + -1.224489796 Combine like terms: 0 + -1.224489796 = -1.224489796 4.693877551t + t2 = -1.224489796 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 = -1.224489796 + 5.508121618 Reorder the terms: 5.508121618 + 4.693877551t + t2 = -1.224489796 + 5.508121618 Combine like terms: -1.224489796 + 5.508121618 = 4.283631822 5.508121618 + 4.693877551t + t2 = 4.283631822 Factor a perfect square on the left side: (t + 2.346938776)(t + 2.346938776) = 4.283631822 Calculate the square root of the right side: 2.069693654 Break this problem into two subproblems by setting (t + 2.346938776) equal to 2.069693654 and -2.069693654.Subproblem 1
t + 2.346938776 = 2.069693654 Simplifying t + 2.346938776 = 2.069693654 Reorder the terms: 2.346938776 + t = 2.069693654 Solving 2.346938776 + t = 2.069693654 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 = 2.069693654 + -2.346938776 Combine like terms: 2.346938776 + -2.346938776 = 0.000000000 0.000000000 + t = 2.069693654 + -2.346938776 t = 2.069693654 + -2.346938776 Combine like terms: 2.069693654 + -2.346938776 = -0.277245122 t = -0.277245122 Simplifying t = -0.277245122Subproblem 2
t + 2.346938776 = -2.069693654 Simplifying t + 2.346938776 = -2.069693654 Reorder the terms: 2.346938776 + t = -2.069693654 Solving 2.346938776 + t = -2.069693654 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 = -2.069693654 + -2.346938776 Combine like terms: 2.346938776 + -2.346938776 = 0.000000000 0.000000000 + t = -2.069693654 + -2.346938776 t = -2.069693654 + -2.346938776 Combine like terms: -2.069693654 + -2.346938776 = -4.41663243 t = -4.41663243 Simplifying t = -4.41663243Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.277245122, -4.41663243}
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