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Simplifying -16t2 + 85t + 10 = 20 Reorder the terms: 10 + 85t + -16t2 = 20 Solving 10 + 85t + -16t2 = 20 Solving for variable 't'. Reorder the terms: 10 + -20 + 85t + -16t2 = 20 + -20 Combine like terms: 10 + -20 = -10 -10 + 85t + -16t2 = 20 + -20 Combine like terms: 20 + -20 = 0 -10 + 85t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 0.625 + -5.3125t + t2 = 0 Move the constant term to the right: Add '-0.625' to each side of the equation. 0.625 + -5.3125t + -0.625 + t2 = 0 + -0.625 Reorder the terms: 0.625 + -0.625 + -5.3125t + t2 = 0 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + -5.3125t + t2 = 0 + -0.625 -5.3125t + t2 = 0 + -0.625 Combine like terms: 0 + -0.625 = -0.625 -5.3125t + t2 = -0.625 The t term is -5.3125t. Take half its coefficient (-2.65625). Square it (7.055664063) and add it to both sides. Add '7.055664063' to each side of the equation. -5.3125t + 7.055664063 + t2 = -0.625 + 7.055664063 Reorder the terms: 7.055664063 + -5.3125t + t2 = -0.625 + 7.055664063 Combine like terms: -0.625 + 7.055664063 = 6.430664063 7.055664063 + -5.3125t + t2 = 6.430664063 Factor a perfect square on the left side: (t + -2.65625)(t + -2.65625) = 6.430664063 Calculate the square root of the right side: 2.535875404 Break this problem into two subproblems by setting (t + -2.65625) equal to 2.535875404 and -2.535875404.Subproblem 1
t + -2.65625 = 2.535875404 Simplifying t + -2.65625 = 2.535875404 Reorder the terms: -2.65625 + t = 2.535875404 Solving -2.65625 + t = 2.535875404 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.65625' to each side of the equation. -2.65625 + 2.65625 + t = 2.535875404 + 2.65625 Combine like terms: -2.65625 + 2.65625 = 0.00000 0.00000 + t = 2.535875404 + 2.65625 t = 2.535875404 + 2.65625 Combine like terms: 2.535875404 + 2.65625 = 5.192125404 t = 5.192125404 Simplifying t = 5.192125404Subproblem 2
t + -2.65625 = -2.535875404 Simplifying t + -2.65625 = -2.535875404 Reorder the terms: -2.65625 + t = -2.535875404 Solving -2.65625 + t = -2.535875404 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.65625' to each side of the equation. -2.65625 + 2.65625 + t = -2.535875404 + 2.65625 Combine like terms: -2.65625 + 2.65625 = 0.00000 0.00000 + t = -2.535875404 + 2.65625 t = -2.535875404 + 2.65625 Combine like terms: -2.535875404 + 2.65625 = 0.120374596 t = 0.120374596 Simplifying t = 0.120374596Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.192125404, 0.120374596}
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