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Simplifying -14t2 + 56t + 9 = 0 Reorder the terms: 9 + 56t + -14t2 = 0 Solving 9 + 56t + -14t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -14 the coefficient of the squared term: Divide each side by '-14'. -0.6428571429 + -4t + t2 = 0 Move the constant term to the right: Add '0.6428571429' to each side of the equation. -0.6428571429 + -4t + 0.6428571429 + t2 = 0 + 0.6428571429 Reorder the terms: -0.6428571429 + 0.6428571429 + -4t + t2 = 0 + 0.6428571429 Combine like terms: -0.6428571429 + 0.6428571429 = 0.0000000000 0.0000000000 + -4t + t2 = 0 + 0.6428571429 -4t + t2 = 0 + 0.6428571429 Combine like terms: 0 + 0.6428571429 = 0.6428571429 -4t + t2 = 0.6428571429 The t term is -4t. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4t + 4 + t2 = 0.6428571429 + 4 Reorder the terms: 4 + -4t + t2 = 0.6428571429 + 4 Combine like terms: 0.6428571429 + 4 = 4.6428571429 4 + -4t + t2 = 4.6428571429 Factor a perfect square on the left side: (t + -2)(t + -2) = 4.6428571429 Calculate the square root of the right side: 2.154729018 Break this problem into two subproblems by setting (t + -2) equal to 2.154729018 and -2.154729018.Subproblem 1
t + -2 = 2.154729018 Simplifying t + -2 = 2.154729018 Reorder the terms: -2 + t = 2.154729018 Solving -2 + t = 2.154729018 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 2.154729018 + 2 Combine like terms: -2 + 2 = 0 0 + t = 2.154729018 + 2 t = 2.154729018 + 2 Combine like terms: 2.154729018 + 2 = 4.154729018 t = 4.154729018 Simplifying t = 4.154729018Subproblem 2
t + -2 = -2.154729018 Simplifying t + -2 = -2.154729018 Reorder the terms: -2 + t = -2.154729018 Solving -2 + t = -2.154729018 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -2.154729018 + 2 Combine like terms: -2 + 2 = 0 0 + t = -2.154729018 + 2 t = -2.154729018 + 2 Combine like terms: -2.154729018 + 2 = -0.154729018 t = -0.154729018 Simplifying t = -0.154729018Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.154729018, -0.154729018}
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