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Simplifying 4t2 + -2t + -8 = 0 Reorder the terms: -8 + -2t + 4t2 = 0 Solving -8 + -2t + 4t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + -1t + 2t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -1t + 2t2)' equal to zero and attempt to solve: Simplifying -4 + -1t + 2t2 = 0 Solving -4 + -1t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2 + -0.5t + t2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -0.5t + 2 + t2 = 0 + 2 Reorder the terms: -2 + 2 + -0.5t + t2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -0.5t + t2 = 0 + 2 -0.5t + t2 = 0 + 2 Combine like terms: 0 + 2 = 2 -0.5t + t2 = 2 The t term is -0.5t. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5t + 0.0625 + t2 = 2 + 0.0625 Reorder the terms: 0.0625 + -0.5t + t2 = 2 + 0.0625 Combine like terms: 2 + 0.0625 = 2.0625 0.0625 + -0.5t + t2 = 2.0625 Factor a perfect square on the left side: (t + -0.25)(t + -0.25) = 2.0625 Calculate the square root of the right side: 1.436140662 Break this problem into two subproblems by setting (t + -0.25) equal to 1.436140662 and -1.436140662.Subproblem 1
t + -0.25 = 1.436140662 Simplifying t + -0.25 = 1.436140662 Reorder the terms: -0.25 + t = 1.436140662 Solving -0.25 + t = 1.436140662 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + t = 1.436140662 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + t = 1.436140662 + 0.25 t = 1.436140662 + 0.25 Combine like terms: 1.436140662 + 0.25 = 1.686140662 t = 1.686140662 Simplifying t = 1.686140662Subproblem 2
t + -0.25 = -1.436140662 Simplifying t + -0.25 = -1.436140662 Reorder the terms: -0.25 + t = -1.436140662 Solving -0.25 + t = -1.436140662 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + t = -1.436140662 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + t = -1.436140662 + 0.25 t = -1.436140662 + 0.25 Combine like terms: -1.436140662 + 0.25 = -1.186140662 t = -1.186140662 Simplifying t = -1.186140662Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.686140662, -1.186140662}Solution
t = {1.686140662, -1.186140662}
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