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Simplifying 0 = -16t2 + 17t + 12 Reorder the terms: 0 = 12 + 17t + -16t2 Solving 0 = 12 + 17t + -16t2 Solving for variable 't'. Combine like terms: 0 + -12 = -12 -12 + -17t + 16t2 = 12 + 17t + -16t2 + -12 + -17t + 16t2 Reorder the terms: -12 + -17t + 16t2 = 12 + -12 + 17t + -17t + -16t2 + 16t2 Combine like terms: 12 + -12 = 0 -12 + -17t + 16t2 = 0 + 17t + -17t + -16t2 + 16t2 -12 + -17t + 16t2 = 17t + -17t + -16t2 + 16t2 Combine like terms: 17t + -17t = 0 -12 + -17t + 16t2 = 0 + -16t2 + 16t2 -12 + -17t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -12 + -17t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.75 + -1.0625t + t2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -1.0625t + 0.75 + t2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -1.0625t + t2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -1.0625t + t2 = 0 + 0.75 -1.0625t + t2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -1.0625t + t2 = 0.75 The t term is -1.0625t. Take half its coefficient (-0.53125). Square it (0.2822265625) and add it to both sides. Add '0.2822265625' to each side of the equation. -1.0625t + 0.2822265625 + t2 = 0.75 + 0.2822265625 Reorder the terms: 0.2822265625 + -1.0625t + t2 = 0.75 + 0.2822265625 Combine like terms: 0.75 + 0.2822265625 = 1.0322265625 0.2822265625 + -1.0625t + t2 = 1.0322265625 Factor a perfect square on the left side: (t + -0.53125)(t + -0.53125) = 1.0322265625 Calculate the square root of the right side: 1.015985513 Break this problem into two subproblems by setting (t + -0.53125) equal to 1.015985513 and -1.015985513.Subproblem 1
t + -0.53125 = 1.015985513 Simplifying t + -0.53125 = 1.015985513 Reorder the terms: -0.53125 + t = 1.015985513 Solving -0.53125 + t = 1.015985513 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.53125' to each side of the equation. -0.53125 + 0.53125 + t = 1.015985513 + 0.53125 Combine like terms: -0.53125 + 0.53125 = 0.00000 0.00000 + t = 1.015985513 + 0.53125 t = 1.015985513 + 0.53125 Combine like terms: 1.015985513 + 0.53125 = 1.547235513 t = 1.547235513 Simplifying t = 1.547235513Subproblem 2
t + -0.53125 = -1.015985513 Simplifying t + -0.53125 = -1.015985513 Reorder the terms: -0.53125 + t = -1.015985513 Solving -0.53125 + t = -1.015985513 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.53125' to each side of the equation. -0.53125 + 0.53125 + t = -1.015985513 + 0.53125 Combine like terms: -0.53125 + 0.53125 = 0.00000 0.00000 + t = -1.015985513 + 0.53125 t = -1.015985513 + 0.53125 Combine like terms: -1.015985513 + 0.53125 = -0.484735513 t = -0.484735513 Simplifying t = -0.484735513Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.547235513, -0.484735513}
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