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Simplifying 0 = -16t2 + 152t + 386 Reorder the terms: 0 = 386 + 152t + -16t2 Solving 0 = 386 + 152t + -16t2 Solving for variable 't'. Combine like terms: 0 + -386 = -386 -386 + -152t + 16t2 = 386 + 152t + -16t2 + -386 + -152t + 16t2 Reorder the terms: -386 + -152t + 16t2 = 386 + -386 + 152t + -152t + -16t2 + 16t2 Combine like terms: 386 + -386 = 0 -386 + -152t + 16t2 = 0 + 152t + -152t + -16t2 + 16t2 -386 + -152t + 16t2 = 152t + -152t + -16t2 + 16t2 Combine like terms: 152t + -152t = 0 -386 + -152t + 16t2 = 0 + -16t2 + 16t2 -386 + -152t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -386 + -152t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-193 + -76t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-193 + -76t + 8t2)' equal to zero and attempt to solve: Simplifying -193 + -76t + 8t2 = 0 Solving -193 + -76t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -24.125 + -9.5t + t2 = 0 Move the constant term to the right: Add '24.125' to each side of the equation. -24.125 + -9.5t + 24.125 + t2 = 0 + 24.125 Reorder the terms: -24.125 + 24.125 + -9.5t + t2 = 0 + 24.125 Combine like terms: -24.125 + 24.125 = 0.000 0.000 + -9.5t + t2 = 0 + 24.125 -9.5t + t2 = 0 + 24.125 Combine like terms: 0 + 24.125 = 24.125 -9.5t + t2 = 24.125 The t term is -9.5t. Take half its coefficient (-4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. -9.5t + 22.5625 + t2 = 24.125 + 22.5625 Reorder the terms: 22.5625 + -9.5t + t2 = 24.125 + 22.5625 Combine like terms: 24.125 + 22.5625 = 46.6875 22.5625 + -9.5t + t2 = 46.6875 Factor a perfect square on the left side: (t + -4.75)(t + -4.75) = 46.6875 Calculate the square root of the right side: 6.832825184 Break this problem into two subproblems by setting (t + -4.75) equal to 6.832825184 and -6.832825184.Subproblem 1
t + -4.75 = 6.832825184 Simplifying t + -4.75 = 6.832825184 Reorder the terms: -4.75 + t = 6.832825184 Solving -4.75 + t = 6.832825184 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + t = 6.832825184 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + t = 6.832825184 + 4.75 t = 6.832825184 + 4.75 Combine like terms: 6.832825184 + 4.75 = 11.582825184 t = 11.582825184 Simplifying t = 11.582825184Subproblem 2
t + -4.75 = -6.832825184 Simplifying t + -4.75 = -6.832825184 Reorder the terms: -4.75 + t = -6.832825184 Solving -4.75 + t = -6.832825184 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + t = -6.832825184 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + t = -6.832825184 + 4.75 t = -6.832825184 + 4.75 Combine like terms: -6.832825184 + 4.75 = -2.082825184 t = -2.082825184 Simplifying t = -2.082825184Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.582825184, -2.082825184}Solution
t = {11.582825184, -2.082825184}
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