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Simplifying 8t2 + -2t + -12 = 0 Reorder the terms: -12 + -2t + 8t2 = 0 Solving -12 + -2t + 8t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + -1t + 4t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + -1t + 4t2)' equal to zero and attempt to solve: Simplifying -6 + -1t + 4t2 = 0 Solving -6 + -1t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.5 + -0.25t + t2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -0.25t + 1.5 + t2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -0.25t + t2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -0.25t + t2 = 0 + 1.5 -0.25t + t2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -0.25t + t2 = 1.5 The t term is -0.25t. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25t + 0.015625 + t2 = 1.5 + 0.015625 Reorder the terms: 0.015625 + -0.25t + t2 = 1.5 + 0.015625 Combine like terms: 1.5 + 0.015625 = 1.515625 0.015625 + -0.25t + t2 = 1.515625 Factor a perfect square on the left side: (t + -0.125)(t + -0.125) = 1.515625 Calculate the square root of the right side: 1.231107225 Break this problem into two subproblems by setting (t + -0.125) equal to 1.231107225 and -1.231107225.Subproblem 1
t + -0.125 = 1.231107225 Simplifying t + -0.125 = 1.231107225 Reorder the terms: -0.125 + t = 1.231107225 Solving -0.125 + t = 1.231107225 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + t = 1.231107225 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + t = 1.231107225 + 0.125 t = 1.231107225 + 0.125 Combine like terms: 1.231107225 + 0.125 = 1.356107225 t = 1.356107225 Simplifying t = 1.356107225Subproblem 2
t + -0.125 = -1.231107225 Simplifying t + -0.125 = -1.231107225 Reorder the terms: -0.125 + t = -1.231107225 Solving -0.125 + t = -1.231107225 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + t = -1.231107225 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + t = -1.231107225 + 0.125 t = -1.231107225 + 0.125 Combine like terms: -1.231107225 + 0.125 = -1.106107225 t = -1.106107225 Simplifying t = -1.106107225Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.356107225, -1.106107225}Solution
t = {1.356107225, -1.106107225}
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