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Simplifying 16t2 + -35t + 18 = 0 Reorder the terms: 18 + -35t + 16t2 = 0 Solving 18 + -35t + 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'. 1.125 + -2.1875t + t2 = 0 Move the constant term to the right: Add '-1.125' to each side of the equation. 1.125 + -2.1875t + -1.125 + t2 = 0 + -1.125 Reorder the terms: 1.125 + -1.125 + -2.1875t + t2 = 0 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + -2.1875t + t2 = 0 + -1.125 -2.1875t + t2 = 0 + -1.125 Combine like terms: 0 + -1.125 = -1.125 -2.1875t + t2 = -1.125 The t term is -2.1875t. Take half its coefficient (-1.09375). Square it (1.196289063) and add it to both sides. Add '1.196289063' to each side of the equation. -2.1875t + 1.196289063 + t2 = -1.125 + 1.196289063 Reorder the terms: 1.196289063 + -2.1875t + t2 = -1.125 + 1.196289063 Combine like terms: -1.125 + 1.196289063 = 0.071289063 1.196289063 + -2.1875t + t2 = 0.071289063 Factor a perfect square on the left side: (t + -1.09375)(t + -1.09375) = 0.071289063 Calculate the square root of the right side: 0.267000118 Break this problem into two subproblems by setting (t + -1.09375) equal to 0.267000118 and -0.267000118.Subproblem 1
t + -1.09375 = 0.267000118 Simplifying t + -1.09375 = 0.267000118 Reorder the terms: -1.09375 + t = 0.267000118 Solving -1.09375 + t = 0.267000118 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.09375' to each side of the equation. -1.09375 + 1.09375 + t = 0.267000118 + 1.09375 Combine like terms: -1.09375 + 1.09375 = 0.00000 0.00000 + t = 0.267000118 + 1.09375 t = 0.267000118 + 1.09375 Combine like terms: 0.267000118 + 1.09375 = 1.360750118 t = 1.360750118 Simplifying t = 1.360750118Subproblem 2
t + -1.09375 = -0.267000118 Simplifying t + -1.09375 = -0.267000118 Reorder the terms: -1.09375 + t = -0.267000118 Solving -1.09375 + t = -0.267000118 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.09375' to each side of the equation. -1.09375 + 1.09375 + t = -0.267000118 + 1.09375 Combine like terms: -1.09375 + 1.09375 = 0.00000 0.00000 + t = -0.267000118 + 1.09375 t = -0.267000118 + 1.09375 Combine like terms: -0.267000118 + 1.09375 = 0.826749882 t = 0.826749882 Simplifying t = 0.826749882Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.360750118, 0.826749882}
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