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Simplifying (-16t2) + 64t + 4 = 0 Reorder the terms: 4 + 64t + (-16t2) = 0 Solving 4 + 64t + (-16t2) = 0 Solving for variable 't'. 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 = 4.25 4 + -4t + t2 = 4.25 Factor a perfect square on the left side: ((t) + -2)((t) + -2) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting ((t) + -2) equal to 2.061552813 and -2.061552813.Subproblem 1
(t) + -2 = 2.061552813 Simplifying (t) + -2 = 2.061552813 t + -2 = 2.061552813 Reorder the terms: -2 + t = 2.061552813 Solving -2 + t = 2.061552813 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 = 2.061552813 + 2 Combine like terms: -2 + 2 = 0 0 + t = 2.061552813 + 2 t = 2.061552813 + 2 Combine like terms: 2.061552813 + 2 = 4.061552813 t = 4.061552813 Simplifying t = 4.061552813Subproblem 2
(t) + -2 = -2.061552813 Simplifying (t) + -2 = -2.061552813 t + -2 = -2.061552813 Reorder the terms: -2 + t = -2.061552813 Solving -2 + t = -2.061552813 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 = -2.061552813 + 2 Combine like terms: -2 + 2 = 0 0 + t = -2.061552813 + 2 t = -2.061552813 + 2 Combine like terms: -2.061552813 + 2 = -0.061552813 t = -0.061552813 Simplifying t = -0.061552813Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.061552813, -0.061552813}Solution
t = {4.061552813, -0.061552813}
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