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Simplifying -16t2 + -128t + 50 = 0 Reorder the terms: 50 + -128t + -16t2 = 0 Solving 50 + -128t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(25 + -64t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(25 + -64t + -8t2)' equal to zero and attempt to solve: Simplifying 25 + -64t + -8t2 = 0 Solving 25 + -64t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -3.125 + 8t + t2 = 0 Move the constant term to the right: Add '3.125' to each side of the equation. -3.125 + 8t + 3.125 + t2 = 0 + 3.125 Reorder the terms: -3.125 + 3.125 + 8t + t2 = 0 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + 8t + t2 = 0 + 3.125 8t + t2 = 0 + 3.125 Combine like terms: 0 + 3.125 = 3.125 8t + t2 = 3.125 The t term is 8t. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8t + 16 + t2 = 3.125 + 16 Reorder the terms: 16 + 8t + t2 = 3.125 + 16 Combine like terms: 3.125 + 16 = 19.125 16 + 8t + t2 = 19.125 Factor a perfect square on the left side: (t + 4)(t + 4) = 19.125 Calculate the square root of the right side: 4.373213921 Break this problem into two subproblems by setting (t + 4) equal to 4.373213921 and -4.373213921.Subproblem 1
t + 4 = 4.373213921 Simplifying t + 4 = 4.373213921 Reorder the terms: 4 + t = 4.373213921 Solving 4 + t = 4.373213921 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + t = 4.373213921 + -4 Combine like terms: 4 + -4 = 0 0 + t = 4.373213921 + -4 t = 4.373213921 + -4 Combine like terms: 4.373213921 + -4 = 0.373213921 t = 0.373213921 Simplifying t = 0.373213921Subproblem 2
t + 4 = -4.373213921 Simplifying t + 4 = -4.373213921 Reorder the terms: 4 + t = -4.373213921 Solving 4 + t = -4.373213921 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + t = -4.373213921 + -4 Combine like terms: 4 + -4 = 0 0 + t = -4.373213921 + -4 t = -4.373213921 + -4 Combine like terms: -4.373213921 + -4 = -8.373213921 t = -8.373213921 Simplifying t = -8.373213921Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.373213921, -8.373213921}Solution
t = {0.373213921, -8.373213921}
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