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Simplifying 0 = -16t2 + 160t + 4 Reorder the terms: 0 = 4 + 160t + -16t2 Solving 0 = 4 + 160t + -16t2 Solving for variable 't'. Combine like terms: 0 + -4 = -4 -4 + -160t + 16t2 = 4 + 160t + -16t2 + -4 + -160t + 16t2 Reorder the terms: -4 + -160t + 16t2 = 4 + -4 + 160t + -160t + -16t2 + 16t2 Combine like terms: 4 + -4 = 0 -4 + -160t + 16t2 = 0 + 160t + -160t + -16t2 + 16t2 -4 + -160t + 16t2 = 160t + -160t + -16t2 + 16t2 Combine like terms: 160t + -160t = 0 -4 + -160t + 16t2 = 0 + -16t2 + 16t2 -4 + -160t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -4 + -160t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-1 + -40t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + -40t + 4t2)' equal to zero and attempt to solve: Simplifying -1 + -40t + 4t2 = 0 Solving -1 + -40t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.25 + -10t + t2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -10t + 0.25 + t2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -10t + t2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -10t + t2 = 0 + 0.25 -10t + t2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -10t + t2 = 0.25 The t term is -10t. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10t + 25 + t2 = 0.25 + 25 Reorder the terms: 25 + -10t + t2 = 0.25 + 25 Combine like terms: 0.25 + 25 = 25.25 25 + -10t + t2 = 25.25 Factor a perfect square on the left side: (t + -5)(t + -5) = 25.25 Calculate the square root of the right side: 5.024937811 Break this problem into two subproblems by setting (t + -5) equal to 5.024937811 and -5.024937811.Subproblem 1
t + -5 = 5.024937811 Simplifying t + -5 = 5.024937811 Reorder the terms: -5 + t = 5.024937811 Solving -5 + t = 5.024937811 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = 5.024937811 + 5 Combine like terms: -5 + 5 = 0 0 + t = 5.024937811 + 5 t = 5.024937811 + 5 Combine like terms: 5.024937811 + 5 = 10.024937811 t = 10.024937811 Simplifying t = 10.024937811Subproblem 2
t + -5 = -5.024937811 Simplifying t + -5 = -5.024937811 Reorder the terms: -5 + t = -5.024937811 Solving -5 + t = -5.024937811 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = -5.024937811 + 5 Combine like terms: -5 + 5 = 0 0 + t = -5.024937811 + 5 t = -5.024937811 + 5 Combine like terms: -5.024937811 + 5 = -0.024937811 t = -0.024937811 Simplifying t = -0.024937811Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.024937811, -0.024937811}Solution
t = {10.024937811, -0.024937811}
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