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Simplifying 130 = -16t2 + 112t + 6 Reorder the terms: 130 = 6 + 112t + -16t2 Solving 130 = 6 + 112t + -16t2 Solving for variable 't'. Combine like terms: 130 + -6 = 124 124 + -112t + 16t2 = 6 + 112t + -16t2 + -6 + -112t + 16t2 Reorder the terms: 124 + -112t + 16t2 = 6 + -6 + 112t + -112t + -16t2 + 16t2 Combine like terms: 6 + -6 = 0 124 + -112t + 16t2 = 0 + 112t + -112t + -16t2 + 16t2 124 + -112t + 16t2 = 112t + -112t + -16t2 + 16t2 Combine like terms: 112t + -112t = 0 124 + -112t + 16t2 = 0 + -16t2 + 16t2 124 + -112t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 124 + -112t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(31 + -28t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(31 + -28t + 4t2)' equal to zero and attempt to solve: Simplifying 31 + -28t + 4t2 = 0 Solving 31 + -28t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 7.75 + -7t + t2 = 0 Move the constant term to the right: Add '-7.75' to each side of the equation. 7.75 + -7t + -7.75 + t2 = 0 + -7.75 Reorder the terms: 7.75 + -7.75 + -7t + t2 = 0 + -7.75 Combine like terms: 7.75 + -7.75 = 0.00 0.00 + -7t + t2 = 0 + -7.75 -7t + t2 = 0 + -7.75 Combine like terms: 0 + -7.75 = -7.75 -7t + t2 = -7.75 The t term is -7t. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7t + 12.25 + t2 = -7.75 + 12.25 Reorder the terms: 12.25 + -7t + t2 = -7.75 + 12.25 Combine like terms: -7.75 + 12.25 = 4.5 12.25 + -7t + t2 = 4.5 Factor a perfect square on the left side: (t + -3.5)(t + -3.5) = 4.5 Calculate the square root of the right side: 2.121320344 Break this problem into two subproblems by setting (t + -3.5) equal to 2.121320344 and -2.121320344.Subproblem 1
t + -3.5 = 2.121320344 Simplifying t + -3.5 = 2.121320344 Reorder the terms: -3.5 + t = 2.121320344 Solving -3.5 + t = 2.121320344 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + t = 2.121320344 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = 2.121320344 + 3.5 t = 2.121320344 + 3.5 Combine like terms: 2.121320344 + 3.5 = 5.621320344 t = 5.621320344 Simplifying t = 5.621320344Subproblem 2
t + -3.5 = -2.121320344 Simplifying t + -3.5 = -2.121320344 Reorder the terms: -3.5 + t = -2.121320344 Solving -3.5 + t = -2.121320344 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + t = -2.121320344 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = -2.121320344 + 3.5 t = -2.121320344 + 3.5 Combine like terms: -2.121320344 + 3.5 = 1.378679656 t = 1.378679656 Simplifying t = 1.378679656Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.621320344, 1.378679656}Solution
t = {5.621320344, 1.378679656}
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