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Simplifying 16t2 + 160t + 4 = 0 Reorder the terms: 4 + 160t + 16t2 = 0 Solving 4 + 160t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(1 + 40t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + 40t + 4t2)' equal to zero and attempt to solve: Simplifying 1 + 40t + 4t2 = 0 Solving 1 + 40t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.25 + 10t + t2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 10t + -0.25 + t2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 10t + t2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 10t + t2 = 0 + -0.25 10t + t2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 10t + t2 = -0.25 The t term is 10t. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10t + 25 + t2 = -0.25 + 25 Reorder the terms: 25 + 10t + t2 = -0.25 + 25 Combine like terms: -0.25 + 25 = 24.75 25 + 10t + t2 = 24.75 Factor a perfect square on the left side: (t + 5)(t + 5) = 24.75 Calculate the square root of the right side: 4.974937186 Break this problem into two subproblems by setting (t + 5) equal to 4.974937186 and -4.974937186.Subproblem 1
t + 5 = 4.974937186 Simplifying t + 5 = 4.974937186 Reorder the terms: 5 + t = 4.974937186 Solving 5 + t = 4.974937186 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + t = 4.974937186 + -5 Combine like terms: 5 + -5 = 0 0 + t = 4.974937186 + -5 t = 4.974937186 + -5 Combine like terms: 4.974937186 + -5 = -0.025062814 t = -0.025062814 Simplifying t = -0.025062814Subproblem 2
t + 5 = -4.974937186 Simplifying t + 5 = -4.974937186 Reorder the terms: 5 + t = -4.974937186 Solving 5 + t = -4.974937186 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + t = -4.974937186 + -5 Combine like terms: 5 + -5 = 0 0 + t = -4.974937186 + -5 t = -4.974937186 + -5 Combine like terms: -4.974937186 + -5 = -9.974937186 t = -9.974937186 Simplifying t = -9.974937186Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.025062814, -9.974937186}Solution
t = {-0.025062814, -9.974937186}
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