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Simplifying -16t2 + 117t + 310 = 0 Reorder the terms: 310 + 117t + -16t2 = 0 Solving 310 + 117t + -16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -19.375 + -7.3125t + t2 = 0 Move the constant term to the right: Add '19.375' to each side of the equation. -19.375 + -7.3125t + 19.375 + t2 = 0 + 19.375 Reorder the terms: -19.375 + 19.375 + -7.3125t + t2 = 0 + 19.375 Combine like terms: -19.375 + 19.375 = 0.000 0.000 + -7.3125t + t2 = 0 + 19.375 -7.3125t + t2 = 0 + 19.375 Combine like terms: 0 + 19.375 = 19.375 -7.3125t + t2 = 19.375 The t term is -7.3125t. Take half its coefficient (-3.65625). Square it (13.36816406) and add it to both sides. Add '13.36816406' to each side of the equation. -7.3125t + 13.36816406 + t2 = 19.375 + 13.36816406 Reorder the terms: 13.36816406 + -7.3125t + t2 = 19.375 + 13.36816406 Combine like terms: 19.375 + 13.36816406 = 32.74316406 13.36816406 + -7.3125t + t2 = 32.74316406 Factor a perfect square on the left side: (t + -3.65625)(t + -3.65625) = 32.74316406 Calculate the square root of the right side: 5.722164281 Break this problem into two subproblems by setting (t + -3.65625) equal to 5.722164281 and -5.722164281.Subproblem 1
t + -3.65625 = 5.722164281 Simplifying t + -3.65625 = 5.722164281 Reorder the terms: -3.65625 + t = 5.722164281 Solving -3.65625 + t = 5.722164281 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.65625' to each side of the equation. -3.65625 + 3.65625 + t = 5.722164281 + 3.65625 Combine like terms: -3.65625 + 3.65625 = 0.00000 0.00000 + t = 5.722164281 + 3.65625 t = 5.722164281 + 3.65625 Combine like terms: 5.722164281 + 3.65625 = 9.378414281 t = 9.378414281 Simplifying t = 9.378414281Subproblem 2
t + -3.65625 = -5.722164281 Simplifying t + -3.65625 = -5.722164281 Reorder the terms: -3.65625 + t = -5.722164281 Solving -3.65625 + t = -5.722164281 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.65625' to each side of the equation. -3.65625 + 3.65625 + t = -5.722164281 + 3.65625 Combine like terms: -3.65625 + 3.65625 = 0.00000 0.00000 + t = -5.722164281 + 3.65625 t = -5.722164281 + 3.65625 Combine like terms: -5.722164281 + 3.65625 = -2.065914281 t = -2.065914281 Simplifying t = -2.065914281Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.378414281, -2.065914281}
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