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Simplifying -16t2 + 16t + 4 = 0 Reorder the terms: 4 + 16t + -16t2 = 0 Solving 4 + 16t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(1 + 4t + -4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + 4t + -4t2)' equal to zero and attempt to solve: Simplifying 1 + 4t + -4t2 = 0 Solving 1 + 4t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.25 + -1t + t2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -1t + 0.25 + t2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -1t + t2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -1t + t2 = 0 + 0.25 -1t + t2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -1t + t2 = 0.25 The t term is -1t. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1t + 0.25 + t2 = 0.25 + 0.25 Reorder the terms: 0.25 + -1t + t2 = 0.25 + 0.25 Combine like terms: 0.25 + 0.25 = 0.5 0.25 + -1t + t2 = 0.5 Factor a perfect square on the left side: (t + -0.5)(t + -0.5) = 0.5 Calculate the square root of the right side: 0.707106781 Break this problem into two subproblems by setting (t + -0.5) equal to 0.707106781 and -0.707106781.Subproblem 1
t + -0.5 = 0.707106781 Simplifying t + -0.5 = 0.707106781 Reorder the terms: -0.5 + t = 0.707106781 Solving -0.5 + t = 0.707106781 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = 0.707106781 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = 0.707106781 + 0.5 t = 0.707106781 + 0.5 Combine like terms: 0.707106781 + 0.5 = 1.207106781 t = 1.207106781 Simplifying t = 1.207106781Subproblem 2
t + -0.5 = -0.707106781 Simplifying t + -0.5 = -0.707106781 Reorder the terms: -0.5 + t = -0.707106781 Solving -0.5 + t = -0.707106781 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = -0.707106781 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = -0.707106781 + 0.5 t = -0.707106781 + 0.5 Combine like terms: -0.707106781 + 0.5 = -0.207106781 t = -0.207106781 Simplifying t = -0.207106781Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.207106781, -0.207106781}Solution
t = {1.207106781, -0.207106781}
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