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Simplifying 10 = -16t2 + 8t + 48 Reorder the terms: 10 = 48 + 8t + -16t2 Solving 10 = 48 + 8t + -16t2 Solving for variable 't'. Combine like terms: 10 + -48 = -38 -38 + -8t + 16t2 = 48 + 8t + -16t2 + -48 + -8t + 16t2 Reorder the terms: -38 + -8t + 16t2 = 48 + -48 + 8t + -8t + -16t2 + 16t2 Combine like terms: 48 + -48 = 0 -38 + -8t + 16t2 = 0 + 8t + -8t + -16t2 + 16t2 -38 + -8t + 16t2 = 8t + -8t + -16t2 + 16t2 Combine like terms: 8t + -8t = 0 -38 + -8t + 16t2 = 0 + -16t2 + 16t2 -38 + -8t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -38 + -8t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-19 + -4t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-19 + -4t + 8t2)' equal to zero and attempt to solve: Simplifying -19 + -4t + 8t2 = 0 Solving -19 + -4t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.375 + -0.5t + t2 = 0 Move the constant term to the right: Add '2.375' to each side of the equation. -2.375 + -0.5t + 2.375 + t2 = 0 + 2.375 Reorder the terms: -2.375 + 2.375 + -0.5t + t2 = 0 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + -0.5t + t2 = 0 + 2.375 -0.5t + t2 = 0 + 2.375 Combine like terms: 0 + 2.375 = 2.375 -0.5t + t2 = 2.375 The t term is -0.5t. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5t + 0.0625 + t2 = 2.375 + 0.0625 Reorder the terms: 0.0625 + -0.5t + t2 = 2.375 + 0.0625 Combine like terms: 2.375 + 0.0625 = 2.4375 0.0625 + -0.5t + t2 = 2.4375 Factor a perfect square on the left side: (t + -0.25)(t + -0.25) = 2.4375 Calculate the square root of the right side: 1.5612495 Break this problem into two subproblems by setting (t + -0.25) equal to 1.5612495 and -1.5612495.Subproblem 1
t + -0.25 = 1.5612495 Simplifying t + -0.25 = 1.5612495 Reorder the terms: -0.25 + t = 1.5612495 Solving -0.25 + t = 1.5612495 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + t = 1.5612495 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + t = 1.5612495 + 0.25 t = 1.5612495 + 0.25 Combine like terms: 1.5612495 + 0.25 = 1.8112495 t = 1.8112495 Simplifying t = 1.8112495Subproblem 2
t + -0.25 = -1.5612495 Simplifying t + -0.25 = -1.5612495 Reorder the terms: -0.25 + t = -1.5612495 Solving -0.25 + t = -1.5612495 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + t = -1.5612495 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + t = -1.5612495 + 0.25 t = -1.5612495 + 0.25 Combine like terms: -1.5612495 + 0.25 = -1.3112495 t = -1.3112495 Simplifying t = -1.3112495Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.8112495, -1.3112495}Solution
t = {1.8112495, -1.3112495}
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