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Simplifying 0 = -16t2 + -10t + 130 Reorder the terms: 0 = 130 + -10t + -16t2 Solving 0 = 130 + -10t + -16t2 Solving for variable 't'. Combine like terms: 0 + -130 = -130 -130 + 10t + 16t2 = 130 + -10t + -16t2 + -130 + 10t + 16t2 Reorder the terms: -130 + 10t + 16t2 = 130 + -130 + -10t + 10t + -16t2 + 16t2 Combine like terms: 130 + -130 = 0 -130 + 10t + 16t2 = 0 + -10t + 10t + -16t2 + 16t2 -130 + 10t + 16t2 = -10t + 10t + -16t2 + 16t2 Combine like terms: -10t + 10t = 0 -130 + 10t + 16t2 = 0 + -16t2 + 16t2 -130 + 10t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -130 + 10t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-65 + 5t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-65 + 5t + 8t2)' equal to zero and attempt to solve: Simplifying -65 + 5t + 8t2 = 0 Solving -65 + 5t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -8.125 + 0.625t + t2 = 0 Move the constant term to the right: Add '8.125' to each side of the equation. -8.125 + 0.625t + 8.125 + t2 = 0 + 8.125 Reorder the terms: -8.125 + 8.125 + 0.625t + t2 = 0 + 8.125 Combine like terms: -8.125 + 8.125 = 0.000 0.000 + 0.625t + t2 = 0 + 8.125 0.625t + t2 = 0 + 8.125 Combine like terms: 0 + 8.125 = 8.125 0.625t + t2 = 8.125 The t term is 0.625t. Take half its coefficient (0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. 0.625t + 0.09765625 + t2 = 8.125 + 0.09765625 Reorder the terms: 0.09765625 + 0.625t + t2 = 8.125 + 0.09765625 Combine like terms: 8.125 + 0.09765625 = 8.22265625 0.09765625 + 0.625t + t2 = 8.22265625 Factor a perfect square on the left side: (t + 0.3125)(t + 0.3125) = 8.22265625 Calculate the square root of the right side: 2.867517437 Break this problem into two subproblems by setting (t + 0.3125) equal to 2.867517437 and -2.867517437.Subproblem 1
t + 0.3125 = 2.867517437 Simplifying t + 0.3125 = 2.867517437 Reorder the terms: 0.3125 + t = 2.867517437 Solving 0.3125 + t = 2.867517437 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + t = 2.867517437 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + t = 2.867517437 + -0.3125 t = 2.867517437 + -0.3125 Combine like terms: 2.867517437 + -0.3125 = 2.555017437 t = 2.555017437 Simplifying t = 2.555017437Subproblem 2
t + 0.3125 = -2.867517437 Simplifying t + 0.3125 = -2.867517437 Reorder the terms: 0.3125 + t = -2.867517437 Solving 0.3125 + t = -2.867517437 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + t = -2.867517437 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + t = -2.867517437 + -0.3125 t = -2.867517437 + -0.3125 Combine like terms: -2.867517437 + -0.3125 = -3.180017437 t = -3.180017437 Simplifying t = -3.180017437Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.555017437, -3.180017437}Solution
t = {2.555017437, -3.180017437}
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