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Simplifying -2t2 + 16t + 10 = 0 Reorder the terms: 10 + 16t + -2t2 = 0 Solving 10 + 16t + -2t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 8t + -1t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + 8t + -1t2)' equal to zero and attempt to solve: Simplifying 5 + 8t + -1t2 = 0 Solving 5 + 8t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5 + -8t + t2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -8t + 5 + t2 = 0 + 5 Reorder the terms: -5 + 5 + -8t + t2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -8t + t2 = 0 + 5 -8t + t2 = 0 + 5 Combine like terms: 0 + 5 = 5 -8t + t2 = 5 The t term is -8t. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8t + 16 + t2 = 5 + 16 Reorder the terms: 16 + -8t + t2 = 5 + 16 Combine like terms: 5 + 16 = 21 16 + -8t + t2 = 21 Factor a perfect square on the left side: (t + -4)(t + -4) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (t + -4) equal to 4.582575695 and -4.582575695.Subproblem 1
t + -4 = 4.582575695 Simplifying t + -4 = 4.582575695 Reorder the terms: -4 + t = 4.582575695 Solving -4 + t = 4.582575695 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = 4.582575695 + 4 Combine like terms: -4 + 4 = 0 0 + t = 4.582575695 + 4 t = 4.582575695 + 4 Combine like terms: 4.582575695 + 4 = 8.582575695 t = 8.582575695 Simplifying t = 8.582575695Subproblem 2
t + -4 = -4.582575695 Simplifying t + -4 = -4.582575695 Reorder the terms: -4 + t = -4.582575695 Solving -4 + t = -4.582575695 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = -4.582575695 + 4 Combine like terms: -4 + 4 = 0 0 + t = -4.582575695 + 4 t = -4.582575695 + 4 Combine like terms: -4.582575695 + 4 = -0.582575695 t = -0.582575695 Simplifying t = -0.582575695Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.582575695, -0.582575695}Solution
t = {8.582575695, -0.582575695}
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