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Simplifying -16t2 + -17t + 4 = 8 Reorder the terms: 4 + -17t + -16t2 = 8 Solving 4 + -17t + -16t2 = 8 Solving for variable 't'. Reorder the terms: 4 + -8 + -17t + -16t2 = 8 + -8 Combine like terms: 4 + -8 = -4 -4 + -17t + -16t2 = 8 + -8 Combine like terms: 8 + -8 = 0 -4 + -17t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + 17t + 16t2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + 17t + 16t2)' equal to zero and attempt to solve: Simplifying 4 + 17t + 16t2 = 0 Solving 4 + 17t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.25 + 1.0625t + t2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 1.0625t + -0.25 + t2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 1.0625t + t2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 1.0625t + t2 = 0 + -0.25 1.0625t + t2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 1.0625t + t2 = -0.25 The t term is 1.0625t. Take half its coefficient (0.53125). Square it (0.2822265625) and add it to both sides. Add '0.2822265625' to each side of the equation. 1.0625t + 0.2822265625 + t2 = -0.25 + 0.2822265625 Reorder the terms: 0.2822265625 + 1.0625t + t2 = -0.25 + 0.2822265625 Combine like terms: -0.25 + 0.2822265625 = 0.0322265625 0.2822265625 + 1.0625t + t2 = 0.0322265625 Factor a perfect square on the left side: (t + 0.53125)(t + 0.53125) = 0.0322265625 Calculate the square root of the right side: 0.179517583 Break this problem into two subproblems by setting (t + 0.53125) equal to 0.179517583 and -0.179517583.Subproblem 1
t + 0.53125 = 0.179517583 Simplifying t + 0.53125 = 0.179517583 Reorder the terms: 0.53125 + t = 0.179517583 Solving 0.53125 + t = 0.179517583 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.53125' to each side of the equation. 0.53125 + -0.53125 + t = 0.179517583 + -0.53125 Combine like terms: 0.53125 + -0.53125 = 0.00000 0.00000 + t = 0.179517583 + -0.53125 t = 0.179517583 + -0.53125 Combine like terms: 0.179517583 + -0.53125 = -0.351732417 t = -0.351732417 Simplifying t = -0.351732417Subproblem 2
t + 0.53125 = -0.179517583 Simplifying t + 0.53125 = -0.179517583 Reorder the terms: 0.53125 + t = -0.179517583 Solving 0.53125 + t = -0.179517583 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.53125' to each side of the equation. 0.53125 + -0.53125 + t = -0.179517583 + -0.53125 Combine like terms: 0.53125 + -0.53125 = 0.00000 0.00000 + t = -0.179517583 + -0.53125 t = -0.179517583 + -0.53125 Combine like terms: -0.179517583 + -0.53125 = -0.710767583 t = -0.710767583 Simplifying t = -0.710767583Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.351732417, -0.710767583}Solution
t = {-0.351732417, -0.710767583}
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