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Simplifying 0 = -16t2 + 36t + 160 Reorder the terms: 0 = 160 + 36t + -16t2 Solving 0 = 160 + 36t + -16t2 Solving for variable 't'. Combine like terms: 0 + -160 = -160 -160 + -36t + 16t2 = 160 + 36t + -16t2 + -160 + -36t + 16t2 Reorder the terms: -160 + -36t + 16t2 = 160 + -160 + 36t + -36t + -16t2 + 16t2 Combine like terms: 160 + -160 = 0 -160 + -36t + 16t2 = 0 + 36t + -36t + -16t2 + 16t2 -160 + -36t + 16t2 = 36t + -36t + -16t2 + 16t2 Combine like terms: 36t + -36t = 0 -160 + -36t + 16t2 = 0 + -16t2 + 16t2 -160 + -36t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -160 + -36t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-40 + -9t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-40 + -9t + 4t2)' equal to zero and attempt to solve: Simplifying -40 + -9t + 4t2 = 0 Solving -40 + -9t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -10 + -2.25t + t2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -2.25t + 10 + t2 = 0 + 10 Reorder the terms: -10 + 10 + -2.25t + t2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -2.25t + t2 = 0 + 10 -2.25t + t2 = 0 + 10 Combine like terms: 0 + 10 = 10 -2.25t + t2 = 10 The t term is -2.25t. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25t + 1.265625 + t2 = 10 + 1.265625 Reorder the terms: 1.265625 + -2.25t + t2 = 10 + 1.265625 Combine like terms: 10 + 1.265625 = 11.265625 1.265625 + -2.25t + t2 = 11.265625 Factor a perfect square on the left side: (t + -1.125)(t + -1.125) = 11.265625 Calculate the square root of the right side: 3.356430396 Break this problem into two subproblems by setting (t + -1.125) equal to 3.356430396 and -3.356430396.Subproblem 1
t + -1.125 = 3.356430396 Simplifying t + -1.125 = 3.356430396 Reorder the terms: -1.125 + t = 3.356430396 Solving -1.125 + t = 3.356430396 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + t = 3.356430396 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + t = 3.356430396 + 1.125 t = 3.356430396 + 1.125 Combine like terms: 3.356430396 + 1.125 = 4.481430396 t = 4.481430396 Simplifying t = 4.481430396Subproblem 2
t + -1.125 = -3.356430396 Simplifying t + -1.125 = -3.356430396 Reorder the terms: -1.125 + t = -3.356430396 Solving -1.125 + t = -3.356430396 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + t = -3.356430396 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + t = -3.356430396 + 1.125 t = -3.356430396 + 1.125 Combine like terms: -3.356430396 + 1.125 = -2.231430396 t = -2.231430396 Simplifying t = -2.231430396Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.481430396, -2.231430396}Solution
t = {4.481430396, -2.231430396}
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