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Simplifying 10 = -16t2 + 160t + 70 Reorder the terms: 10 = 70 + 160t + -16t2 Solving 10 = 70 + 160t + -16t2 Solving for variable 't'. Combine like terms: 10 + -70 = -60 -60 + -160t + 16t2 = 70 + 160t + -16t2 + -70 + -160t + 16t2 Reorder the terms: -60 + -160t + 16t2 = 70 + -70 + 160t + -160t + -16t2 + 16t2 Combine like terms: 70 + -70 = 0 -60 + -160t + 16t2 = 0 + 160t + -160t + -16t2 + 16t2 -60 + -160t + 16t2 = 160t + -160t + -16t2 + 16t2 Combine like terms: 160t + -160t = 0 -60 + -160t + 16t2 = 0 + -16t2 + 16t2 -60 + -160t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -60 + -160t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-15 + -40t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-15 + -40t + 4t2)' equal to zero and attempt to solve: Simplifying -15 + -40t + 4t2 = 0 Solving -15 + -40t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.75 + -10t + t2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + -10t + 3.75 + t2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + -10t + t2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + -10t + t2 = 0 + 3.75 -10t + t2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 -10t + t2 = 3.75 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 = 3.75 + 25 Reorder the terms: 25 + -10t + t2 = 3.75 + 25 Combine like terms: 3.75 + 25 = 28.75 25 + -10t + t2 = 28.75 Factor a perfect square on the left side: (t + -5)(t + -5) = 28.75 Calculate the square root of the right side: 5.361902647 Break this problem into two subproblems by setting (t + -5) equal to 5.361902647 and -5.361902647.Subproblem 1
t + -5 = 5.361902647 Simplifying t + -5 = 5.361902647 Reorder the terms: -5 + t = 5.361902647 Solving -5 + t = 5.361902647 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 = 5.361902647 + 5 Combine like terms: -5 + 5 = 0 0 + t = 5.361902647 + 5 t = 5.361902647 + 5 Combine like terms: 5.361902647 + 5 = 10.361902647 t = 10.361902647 Simplifying t = 10.361902647Subproblem 2
t + -5 = -5.361902647 Simplifying t + -5 = -5.361902647 Reorder the terms: -5 + t = -5.361902647 Solving -5 + t = -5.361902647 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 = -5.361902647 + 5 Combine like terms: -5 + 5 = 0 0 + t = -5.361902647 + 5 t = -5.361902647 + 5 Combine like terms: -5.361902647 + 5 = -0.361902647 t = -0.361902647 Simplifying t = -0.361902647Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.361902647, -0.361902647}Solution
t = {10.361902647, -0.361902647}
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