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Simplifying 160t + -16t2 + 14 = 0 Reorder the terms: 14 + 160t + -16t2 = 0 Solving 14 + 160t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(7 + 80t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + 80t + -8t2)' equal to zero and attempt to solve: Simplifying 7 + 80t + -8t2 = 0 Solving 7 + 80t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.875 + -10t + t2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + -10t + 0.875 + t2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + -10t + t2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + -10t + t2 = 0 + 0.875 -10t + t2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 -10t + t2 = 0.875 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 = 0.875 + 25 Reorder the terms: 25 + -10t + t2 = 0.875 + 25 Combine like terms: 0.875 + 25 = 25.875 25 + -10t + t2 = 25.875 Factor a perfect square on the left side: (t + -5)(t + -5) = 25.875 Calculate the square root of the right side: 5.086747487 Break this problem into two subproblems by setting (t + -5) equal to 5.086747487 and -5.086747487.Subproblem 1
t + -5 = 5.086747487 Simplifying t + -5 = 5.086747487 Reorder the terms: -5 + t = 5.086747487 Solving -5 + t = 5.086747487 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 = 5.086747487 + 5 Combine like terms: -5 + 5 = 0 0 + t = 5.086747487 + 5 t = 5.086747487 + 5 Combine like terms: 5.086747487 + 5 = 10.086747487 t = 10.086747487 Simplifying t = 10.086747487Subproblem 2
t + -5 = -5.086747487 Simplifying t + -5 = -5.086747487 Reorder the terms: -5 + t = -5.086747487 Solving -5 + t = -5.086747487 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 = -5.086747487 + 5 Combine like terms: -5 + 5 = 0 0 + t = -5.086747487 + 5 t = -5.086747487 + 5 Combine like terms: -5.086747487 + 5 = -0.086747487 t = -0.086747487 Simplifying t = -0.086747487Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.086747487, -0.086747487}Solution
t = {10.086747487, -0.086747487}
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