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Simplifying 48 = 320t + -16t2 Solving 48 = 320t + -16t2 Solving for variable 't'. Reorder the terms: 48 + -320t + 16t2 = 320t + -320t + -16t2 + 16t2 Combine like terms: 320t + -320t = 0 48 + -320t + 16t2 = 0 + -16t2 + 16t2 48 + -320t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 48 + -320t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(3 + -20t + t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(3 + -20t + t2)' equal to zero and attempt to solve: Simplifying 3 + -20t + t2 = 0 Solving 3 + -20t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -20t + -3 + t2 = 0 + -3 Reorder the terms: 3 + -3 + -20t + t2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -20t + t2 = 0 + -3 -20t + t2 = 0 + -3 Combine like terms: 0 + -3 = -3 -20t + t2 = -3 The t term is -20t. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20t + 100 + t2 = -3 + 100 Reorder the terms: 100 + -20t + t2 = -3 + 100 Combine like terms: -3 + 100 = 97 100 + -20t + t2 = 97 Factor a perfect square on the left side: (t + -10)(t + -10) = 97 Calculate the square root of the right side: 9.848857802 Break this problem into two subproblems by setting (t + -10) equal to 9.848857802 and -9.848857802.Subproblem 1
t + -10 = 9.848857802 Simplifying t + -10 = 9.848857802 Reorder the terms: -10 + t = 9.848857802 Solving -10 + t = 9.848857802 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + t = 9.848857802 + 10 Combine like terms: -10 + 10 = 0 0 + t = 9.848857802 + 10 t = 9.848857802 + 10 Combine like terms: 9.848857802 + 10 = 19.848857802 t = 19.848857802 Simplifying t = 19.848857802Subproblem 2
t + -10 = -9.848857802 Simplifying t + -10 = -9.848857802 Reorder the terms: -10 + t = -9.848857802 Solving -10 + t = -9.848857802 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + t = -9.848857802 + 10 Combine like terms: -10 + 10 = 0 0 + t = -9.848857802 + 10 t = -9.848857802 + 10 Combine like terms: -9.848857802 + 10 = 0.151142198 t = 0.151142198 Simplifying t = 0.151142198Solution
The solution to the problem is based on the solutions from the subproblems. t = {19.848857802, 0.151142198}Solution
t = {19.848857802, 0.151142198}
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