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Simplifying 0 = 16t2 + 64t + 4 Reorder the terms: 0 = 4 + 64t + 16t2 Solving 0 = 4 + 64t + 16t2 Solving for variable 't'. Combine like terms: 0 + -4 = -4 -4 + -64t + -16t2 = 4 + 64t + 16t2 + -4 + -64t + -16t2 Reorder the terms: -4 + -64t + -16t2 = 4 + -4 + 64t + -64t + 16t2 + -16t2 Combine like terms: 4 + -4 = 0 -4 + -64t + -16t2 = 0 + 64t + -64t + 16t2 + -16t2 -4 + -64t + -16t2 = 64t + -64t + 16t2 + -16t2 Combine like terms: 64t + -64t = 0 -4 + -64t + -16t2 = 0 + 16t2 + -16t2 -4 + -64t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -4 + -64t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-4'. -4(1 + 16t + 4t2) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(1 + 16t + 4t2)' equal to zero and attempt to solve: Simplifying 1 + 16t + 4t2 = 0 Solving 1 + 16t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.25 + 4t + t2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 4t + -0.25 + t2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 4t + t2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 4t + t2 = 0 + -0.25 4t + t2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 4t + t2 = -0.25 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 = -0.25 + 4 Reorder the terms: 4 + 4t + t2 = -0.25 + 4 Combine like terms: -0.25 + 4 = 3.75 4 + 4t + t2 = 3.75 Factor a perfect square on the left side: (t + 2)(t + 2) = 3.75 Calculate the square root of the right side: 1.936491673 Break this problem into two subproblems by setting (t + 2) equal to 1.936491673 and -1.936491673.Subproblem 1
t + 2 = 1.936491673 Simplifying t + 2 = 1.936491673 Reorder the terms: 2 + t = 1.936491673 Solving 2 + t = 1.936491673 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 = 1.936491673 + -2 Combine like terms: 2 + -2 = 0 0 + t = 1.936491673 + -2 t = 1.936491673 + -2 Combine like terms: 1.936491673 + -2 = -0.063508327 t = -0.063508327 Simplifying t = -0.063508327Subproblem 2
t + 2 = -1.936491673 Simplifying t + 2 = -1.936491673 Reorder the terms: 2 + t = -1.936491673 Solving 2 + t = -1.936491673 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 = -1.936491673 + -2 Combine like terms: 2 + -2 = 0 0 + t = -1.936491673 + -2 t = -1.936491673 + -2 Combine like terms: -1.936491673 + -2 = -3.936491673 t = -3.936491673 Simplifying t = -3.936491673Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.063508327, -3.936491673}Solution
t = {-0.063508327, -3.936491673}
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