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Simplifying 32 + 80t + 16t2 = 0 Solving 32 + 80t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '16'. 16(2 + 5t + t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(2 + 5t + t2)' equal to zero and attempt to solve: Simplifying 2 + 5t + t2 = 0 Solving 2 + 5t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 5t + -2 + t2 = 0 + -2 Reorder the terms: 2 + -2 + 5t + t2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5t + t2 = 0 + -2 5t + t2 = 0 + -2 Combine like terms: 0 + -2 = -2 5t + t2 = -2 The t term is 5t. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5t + 6.25 + t2 = -2 + 6.25 Reorder the terms: 6.25 + 5t + t2 = -2 + 6.25 Combine like terms: -2 + 6.25 = 4.25 6.25 + 5t + t2 = 4.25 Factor a perfect square on the left side: (t + 2.5)(t + 2.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (t + 2.5) equal to 2.061552813 and -2.061552813.Subproblem 1
t + 2.5 = 2.061552813 Simplifying t + 2.5 = 2.061552813 Reorder the terms: 2.5 + t = 2.061552813 Solving 2.5 + t = 2.061552813 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + t = 2.061552813 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + t = 2.061552813 + -2.5 t = 2.061552813 + -2.5 Combine like terms: 2.061552813 + -2.5 = -0.438447187 t = -0.438447187 Simplifying t = -0.438447187Subproblem 2
t + 2.5 = -2.061552813 Simplifying t + 2.5 = -2.061552813 Reorder the terms: 2.5 + t = -2.061552813 Solving 2.5 + t = -2.061552813 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + t = -2.061552813 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + t = -2.061552813 + -2.5 t = -2.061552813 + -2.5 Combine like terms: -2.061552813 + -2.5 = -4.561552813 t = -4.561552813 Simplifying t = -4.561552813Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.438447187, -4.561552813}Solution
t = {-0.438447187, -4.561552813}
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