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Simplifying 0 = -2(8t2 + -2t + -35) Reorder the terms: 0 = -2(-35 + -2t + 8t2) 0 = (-35 * -2 + -2t * -2 + 8t2 * -2) 0 = (70 + 4t + -16t2) Solving 0 = 70 + 4t + -16t2 Solving for variable 't'. Combine like terms: 0 + -70 = -70 -70 + -4t + 16t2 = 70 + 4t + -16t2 + -70 + -4t + 16t2 Reorder the terms: -70 + -4t + 16t2 = 70 + -70 + 4t + -4t + -16t2 + 16t2 Combine like terms: 70 + -70 = 0 -70 + -4t + 16t2 = 0 + 4t + -4t + -16t2 + 16t2 -70 + -4t + 16t2 = 4t + -4t + -16t2 + 16t2 Combine like terms: 4t + -4t = 0 -70 + -4t + 16t2 = 0 + -16t2 + 16t2 -70 + -4t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -70 + -4t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-35 + -2t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-35 + -2t + 8t2)' equal to zero and attempt to solve: Simplifying -35 + -2t + 8t2 = 0 Solving -35 + -2t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -4.375 + -0.25t + t2 = 0 Move the constant term to the right: Add '4.375' to each side of the equation. -4.375 + -0.25t + 4.375 + t2 = 0 + 4.375 Reorder the terms: -4.375 + 4.375 + -0.25t + t2 = 0 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + -0.25t + t2 = 0 + 4.375 -0.25t + t2 = 0 + 4.375 Combine like terms: 0 + 4.375 = 4.375 -0.25t + t2 = 4.375 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 = 4.375 + 0.015625 Reorder the terms: 0.015625 + -0.25t + t2 = 4.375 + 0.015625 Combine like terms: 4.375 + 0.015625 = 4.390625 0.015625 + -0.25t + t2 = 4.390625 Factor a perfect square on the left side: (t + -0.125)(t + -0.125) = 4.390625 Calculate the square root of the right side: 2.095381827 Break this problem into two subproblems by setting (t + -0.125) equal to 2.095381827 and -2.095381827.Subproblem 1
t + -0.125 = 2.095381827 Simplifying t + -0.125 = 2.095381827 Reorder the terms: -0.125 + t = 2.095381827 Solving -0.125 + t = 2.095381827 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 = 2.095381827 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + t = 2.095381827 + 0.125 t = 2.095381827 + 0.125 Combine like terms: 2.095381827 + 0.125 = 2.220381827 t = 2.220381827 Simplifying t = 2.220381827Subproblem 2
t + -0.125 = -2.095381827 Simplifying t + -0.125 = -2.095381827 Reorder the terms: -0.125 + t = -2.095381827 Solving -0.125 + t = -2.095381827 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 = -2.095381827 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + t = -2.095381827 + 0.125 t = -2.095381827 + 0.125 Combine like terms: -2.095381827 + 0.125 = -1.970381827 t = -1.970381827 Simplifying t = -1.970381827Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.220381827, -1.970381827}Solution
t = {2.220381827, -1.970381827}
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