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Simplifying 4t2 + 80t = -44 Reorder the terms: 80t + 4t2 = -44 Solving 80t + 4t2 = -44 Solving for variable 't'. Reorder the terms: 44 + 80t + 4t2 = -44 + 44 Combine like terms: -44 + 44 = 0 44 + 80t + 4t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(11 + 20t + t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(11 + 20t + t2)' equal to zero and attempt to solve: Simplifying 11 + 20t + t2 = 0 Solving 11 + 20t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + 20t + -11 + t2 = 0 + -11 Reorder the terms: 11 + -11 + 20t + t2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 20t + t2 = 0 + -11 20t + t2 = 0 + -11 Combine like terms: 0 + -11 = -11 20t + t2 = -11 The t term is 20t. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20t + 100 + t2 = -11 + 100 Reorder the terms: 100 + 20t + t2 = -11 + 100 Combine like terms: -11 + 100 = 89 100 + 20t + t2 = 89 Factor a perfect square on the left side: (t + 10)(t + 10) = 89 Calculate the square root of the right side: 9.433981132 Break this problem into two subproblems by setting (t + 10) equal to 9.433981132 and -9.433981132.Subproblem 1
t + 10 = 9.433981132 Simplifying t + 10 = 9.433981132 Reorder the terms: 10 + t = 9.433981132 Solving 10 + t = 9.433981132 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + t = 9.433981132 + -10 Combine like terms: 10 + -10 = 0 0 + t = 9.433981132 + -10 t = 9.433981132 + -10 Combine like terms: 9.433981132 + -10 = -0.566018868 t = -0.566018868 Simplifying t = -0.566018868Subproblem 2
t + 10 = -9.433981132 Simplifying t + 10 = -9.433981132 Reorder the terms: 10 + t = -9.433981132 Solving 10 + t = -9.433981132 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + t = -9.433981132 + -10 Combine like terms: 10 + -10 = 0 0 + t = -9.433981132 + -10 t = -9.433981132 + -10 Combine like terms: -9.433981132 + -10 = -19.433981132 t = -19.433981132 Simplifying t = -19.433981132Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.566018868, -19.433981132}Solution
t = {-0.566018868, -19.433981132}
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