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Simplifying -16t2 + 113t + 10 = 0 Reorder the terms: 10 + 113t + -16t2 = 0 Solving 10 + 113t + -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'. -0.625 + -7.0625t + t2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -7.0625t + 0.625 + t2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -7.0625t + t2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -7.0625t + t2 = 0 + 0.625 -7.0625t + t2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -7.0625t + t2 = 0.625 The t term is -7.0625t. Take half its coefficient (-3.53125). Square it (12.46972656) and add it to both sides. Add '12.46972656' to each side of the equation. -7.0625t + 12.46972656 + t2 = 0.625 + 12.46972656 Reorder the terms: 12.46972656 + -7.0625t + t2 = 0.625 + 12.46972656 Combine like terms: 0.625 + 12.46972656 = 13.09472656 12.46972656 + -7.0625t + t2 = 13.09472656 Factor a perfect square on the left side: (t + -3.53125)(t + -3.53125) = 13.09472656 Calculate the square root of the right side: 3.618663643 Break this problem into two subproblems by setting (t + -3.53125) equal to 3.618663643 and -3.618663643.Subproblem 1
t + -3.53125 = 3.618663643 Simplifying t + -3.53125 = 3.618663643 Reorder the terms: -3.53125 + t = 3.618663643 Solving -3.53125 + t = 3.618663643 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.53125' to each side of the equation. -3.53125 + 3.53125 + t = 3.618663643 + 3.53125 Combine like terms: -3.53125 + 3.53125 = 0.00000 0.00000 + t = 3.618663643 + 3.53125 t = 3.618663643 + 3.53125 Combine like terms: 3.618663643 + 3.53125 = 7.149913643 t = 7.149913643 Simplifying t = 7.149913643Subproblem 2
t + -3.53125 = -3.618663643 Simplifying t + -3.53125 = -3.618663643 Reorder the terms: -3.53125 + t = -3.618663643 Solving -3.53125 + t = -3.618663643 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.53125' to each side of the equation. -3.53125 + 3.53125 + t = -3.618663643 + 3.53125 Combine like terms: -3.53125 + 3.53125 = 0.00000 0.00000 + t = -3.618663643 + 3.53125 t = -3.618663643 + 3.53125 Combine like terms: -3.618663643 + 3.53125 = -0.087413643 t = -0.087413643 Simplifying t = -0.087413643Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.149913643, -0.087413643}
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