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Simplifying 128t + -16t2 = 10 Solving 128t + -16t2 = 10 Solving for variable 't'. Reorder the terms: -10 + 128t + -16t2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 128t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 64t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + 64t + -8t2)' equal to zero and attempt to solve: Simplifying -5 + 64t + -8t2 = 0 Solving -5 + 64t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 0.625 + -8t + t2 = 0 Move the constant term to the right: Add '-0.625' to each side of the equation. 0.625 + -8t + -0.625 + t2 = 0 + -0.625 Reorder the terms: 0.625 + -0.625 + -8t + t2 = 0 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + -8t + t2 = 0 + -0.625 -8t + t2 = 0 + -0.625 Combine like terms: 0 + -0.625 = -0.625 -8t + t2 = -0.625 The t term is -8t. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8t + 16 + t2 = -0.625 + 16 Reorder the terms: 16 + -8t + t2 = -0.625 + 16 Combine like terms: -0.625 + 16 = 15.375 16 + -8t + t2 = 15.375 Factor a perfect square on the left side: (t + -4)(t + -4) = 15.375 Calculate the square root of the right side: 3.921096785 Break this problem into two subproblems by setting (t + -4) equal to 3.921096785 and -3.921096785.Subproblem 1
t + -4 = 3.921096785 Simplifying t + -4 = 3.921096785 Reorder the terms: -4 + t = 3.921096785 Solving -4 + t = 3.921096785 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = 3.921096785 + 4 Combine like terms: -4 + 4 = 0 0 + t = 3.921096785 + 4 t = 3.921096785 + 4 Combine like terms: 3.921096785 + 4 = 7.921096785 t = 7.921096785 Simplifying t = 7.921096785Subproblem 2
t + -4 = -3.921096785 Simplifying t + -4 = -3.921096785 Reorder the terms: -4 + t = -3.921096785 Solving -4 + t = -3.921096785 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = -3.921096785 + 4 Combine like terms: -4 + 4 = 0 0 + t = -3.921096785 + 4 t = -3.921096785 + 4 Combine like terms: -3.921096785 + 4 = 0.078903215 t = 0.078903215 Simplifying t = 0.078903215Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.921096785, 0.078903215}Solution
t = {7.921096785, 0.078903215}
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