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Simplifying 0 = -16t2 + 208t + 156 Reorder the terms: 0 = 156 + 208t + -16t2 Solving 0 = 156 + 208t + -16t2 Solving for variable 't'. Combine like terms: 0 + -156 = -156 -156 + -208t + 16t2 = 156 + 208t + -16t2 + -156 + -208t + 16t2 Reorder the terms: -156 + -208t + 16t2 = 156 + -156 + 208t + -208t + -16t2 + 16t2 Combine like terms: 156 + -156 = 0 -156 + -208t + 16t2 = 0 + 208t + -208t + -16t2 + 16t2 -156 + -208t + 16t2 = 208t + -208t + -16t2 + 16t2 Combine like terms: 208t + -208t = 0 -156 + -208t + 16t2 = 0 + -16t2 + 16t2 -156 + -208t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -156 + -208t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-39 + -52t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-39 + -52t + 4t2)' equal to zero and attempt to solve: Simplifying -39 + -52t + 4t2 = 0 Solving -39 + -52t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -9.75 + -13t + t2 = 0 Move the constant term to the right: Add '9.75' to each side of the equation. -9.75 + -13t + 9.75 + t2 = 0 + 9.75 Reorder the terms: -9.75 + 9.75 + -13t + t2 = 0 + 9.75 Combine like terms: -9.75 + 9.75 = 0.00 0.00 + -13t + t2 = 0 + 9.75 -13t + t2 = 0 + 9.75 Combine like terms: 0 + 9.75 = 9.75 -13t + t2 = 9.75 The t term is -13t. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13t + 42.25 + t2 = 9.75 + 42.25 Reorder the terms: 42.25 + -13t + t2 = 9.75 + 42.25 Combine like terms: 9.75 + 42.25 = 52 42.25 + -13t + t2 = 52 Factor a perfect square on the left side: (t + -6.5)(t + -6.5) = 52 Calculate the square root of the right side: 7.211102551 Break this problem into two subproblems by setting (t + -6.5) equal to 7.211102551 and -7.211102551.Subproblem 1
t + -6.5 = 7.211102551 Simplifying t + -6.5 = 7.211102551 Reorder the terms: -6.5 + t = 7.211102551 Solving -6.5 + t = 7.211102551 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + t = 7.211102551 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + t = 7.211102551 + 6.5 t = 7.211102551 + 6.5 Combine like terms: 7.211102551 + 6.5 = 13.711102551 t = 13.711102551 Simplifying t = 13.711102551Subproblem 2
t + -6.5 = -7.211102551 Simplifying t + -6.5 = -7.211102551 Reorder the terms: -6.5 + t = -7.211102551 Solving -6.5 + t = -7.211102551 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + t = -7.211102551 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + t = -7.211102551 + 6.5 t = -7.211102551 + 6.5 Combine like terms: -7.211102551 + 6.5 = -0.711102551 t = -0.711102551 Simplifying t = -0.711102551Solution
The solution to the problem is based on the solutions from the subproblems. t = {13.711102551, -0.711102551}Solution
t = {13.711102551, -0.711102551}
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