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Simplifying -16t2 + 10t + 775 = 0 Reorder the terms: 775 + 10t + -16t2 = 0 Solving 775 + 10t + -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'. -48.4375 + -0.625t + t2 = 0 Move the constant term to the right: Add '48.4375' to each side of the equation. -48.4375 + -0.625t + 48.4375 + t2 = 0 + 48.4375 Reorder the terms: -48.4375 + 48.4375 + -0.625t + t2 = 0 + 48.4375 Combine like terms: -48.4375 + 48.4375 = 0.0000 0.0000 + -0.625t + t2 = 0 + 48.4375 -0.625t + t2 = 0 + 48.4375 Combine like terms: 0 + 48.4375 = 48.4375 -0.625t + t2 = 48.4375 The t term is -0.625t. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625t + 0.09765625 + t2 = 48.4375 + 0.09765625 Reorder the terms: 0.09765625 + -0.625t + t2 = 48.4375 + 0.09765625 Combine like terms: 48.4375 + 0.09765625 = 48.53515625 0.09765625 + -0.625t + t2 = 48.53515625 Factor a perfect square on the left side: (t + -0.3125)(t + -0.3125) = 48.53515625 Calculate the square root of the right side: 6.966717753 Break this problem into two subproblems by setting (t + -0.3125) equal to 6.966717753 and -6.966717753.Subproblem 1
t + -0.3125 = 6.966717753 Simplifying t + -0.3125 = 6.966717753 Reorder the terms: -0.3125 + t = 6.966717753 Solving -0.3125 + t = 6.966717753 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + t = 6.966717753 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + t = 6.966717753 + 0.3125 t = 6.966717753 + 0.3125 Combine like terms: 6.966717753 + 0.3125 = 7.279217753 t = 7.279217753 Simplifying t = 7.279217753Subproblem 2
t + -0.3125 = -6.966717753 Simplifying t + -0.3125 = -6.966717753 Reorder the terms: -0.3125 + t = -6.966717753 Solving -0.3125 + t = -6.966717753 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + t = -6.966717753 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + t = -6.966717753 + 0.3125 t = -6.966717753 + 0.3125 Combine like terms: -6.966717753 + 0.3125 = -6.654217753 t = -6.654217753 Simplifying t = -6.654217753Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.279217753, -6.654217753}
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