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Simplifying 0 = 4t2 + 16t + 5 Reorder the terms: 0 = 5 + 16t + 4t2 Solving 0 = 5 + 16t + 4t2 Solving for variable 't'. Combine like terms: 0 + -5 = -5 -5 + -16t + -4t2 = 5 + 16t + 4t2 + -5 + -16t + -4t2 Reorder the terms: -5 + -16t + -4t2 = 5 + -5 + 16t + -16t + 4t2 + -4t2 Combine like terms: 5 + -5 = 0 -5 + -16t + -4t2 = 0 + 16t + -16t + 4t2 + -4t2 -5 + -16t + -4t2 = 16t + -16t + 4t2 + -4t2 Combine like terms: 16t + -16t = 0 -5 + -16t + -4t2 = 0 + 4t2 + -4t2 -5 + -16t + -4t2 = 4t2 + -4t2 Combine like terms: 4t2 + -4t2 = 0 -5 + -16t + -4t2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 16t + 4t2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 16t + 4t2)' equal to zero and attempt to solve: Simplifying 5 + 16t + 4t2 = 0 Solving 5 + 16t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + 4t + t2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + 4t + -1.25 + t2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + 4t + t2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + 4t + t2 = 0 + -1.25 4t + t2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 4t + t2 = -1.25 The t term is 4t. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4t + 4 + t2 = -1.25 + 4 Reorder the terms: 4 + 4t + t2 = -1.25 + 4 Combine like terms: -1.25 + 4 = 2.75 4 + 4t + t2 = 2.75 Factor a perfect square on the left side: (t + 2)(t + 2) = 2.75 Calculate the square root of the right side: 1.658312395 Break this problem into two subproblems by setting (t + 2) equal to 1.658312395 and -1.658312395.Subproblem 1
t + 2 = 1.658312395 Simplifying t + 2 = 1.658312395 Reorder the terms: 2 + t = 1.658312395 Solving 2 + t = 1.658312395 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + t = 1.658312395 + -2 Combine like terms: 2 + -2 = 0 0 + t = 1.658312395 + -2 t = 1.658312395 + -2 Combine like terms: 1.658312395 + -2 = -0.341687605 t = -0.341687605 Simplifying t = -0.341687605Subproblem 2
t + 2 = -1.658312395 Simplifying t + 2 = -1.658312395 Reorder the terms: 2 + t = -1.658312395 Solving 2 + t = -1.658312395 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + t = -1.658312395 + -2 Combine like terms: 2 + -2 = 0 0 + t = -1.658312395 + -2 t = -1.658312395 + -2 Combine like terms: -1.658312395 + -2 = -3.658312395 t = -3.658312395 Simplifying t = -3.658312395Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.341687605, -3.658312395}Solution
t = {-0.341687605, -3.658312395}
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