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Simplifying 0 = 16t2 + 64t + 10 Reorder the terms: 0 = 10 + 64t + 16t2 Solving 0 = 10 + 64t + 16t2 Solving for variable 't'. Combine like terms: 0 + -10 = -10 -10 + -64t + -16t2 = 10 + 64t + 16t2 + -10 + -64t + -16t2 Reorder the terms: -10 + -64t + -16t2 = 10 + -10 + 64t + -64t + 16t2 + -16t2 Combine like terms: 10 + -10 = 0 -10 + -64t + -16t2 = 0 + 64t + -64t + 16t2 + -16t2 -10 + -64t + -16t2 = 64t + -64t + 16t2 + -16t2 Combine like terms: 64t + -64t = 0 -10 + -64t + -16t2 = 0 + 16t2 + -16t2 -10 + -64t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -10 + -64t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(5 + 32t + 8t2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(5 + 32t + 8t2)' equal to zero and attempt to solve: Simplifying 5 + 32t + 8t2 = 0 Solving 5 + 32t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.625 + 4t + t2 = 0 Move the constant term to the right: Add '-0.625' to each side of the equation. 0.625 + 4t + -0.625 + t2 = 0 + -0.625 Reorder the terms: 0.625 + -0.625 + 4t + t2 = 0 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + 4t + t2 = 0 + -0.625 4t + t2 = 0 + -0.625 Combine like terms: 0 + -0.625 = -0.625 4t + t2 = -0.625 The t term is 4t. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4t + 4 + t2 = -0.625 + 4 Reorder the terms: 4 + 4t + t2 = -0.625 + 4 Combine like terms: -0.625 + 4 = 3.375 4 + 4t + t2 = 3.375 Factor a perfect square on the left side: (t + 2)(t + 2) = 3.375 Calculate the square root of the right side: 1.837117307 Break this problem into two subproblems by setting (t + 2) equal to 1.837117307 and -1.837117307.Subproblem 1
t + 2 = 1.837117307 Simplifying t + 2 = 1.837117307 Reorder the terms: 2 + t = 1.837117307 Solving 2 + t = 1.837117307 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + t = 1.837117307 + -2 Combine like terms: 2 + -2 = 0 0 + t = 1.837117307 + -2 t = 1.837117307 + -2 Combine like terms: 1.837117307 + -2 = -0.162882693 t = -0.162882693 Simplifying t = -0.162882693Subproblem 2
t + 2 = -1.837117307 Simplifying t + 2 = -1.837117307 Reorder the terms: 2 + t = -1.837117307 Solving 2 + t = -1.837117307 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + t = -1.837117307 + -2 Combine like terms: 2 + -2 = 0 0 + t = -1.837117307 + -2 t = -1.837117307 + -2 Combine like terms: -1.837117307 + -2 = -3.837117307 t = -3.837117307 Simplifying t = -3.837117307Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.162882693, -3.837117307}Solution
t = {-0.162882693, -3.837117307}
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