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Simplifying 0 = -16t2 + 64t + 190 Reorder the terms: 0 = 190 + 64t + -16t2 Solving 0 = 190 + 64t + -16t2 Solving for variable 't'. Combine like terms: 0 + -190 = -190 -190 + -64t + 16t2 = 190 + 64t + -16t2 + -190 + -64t + 16t2 Reorder the terms: -190 + -64t + 16t2 = 190 + -190 + 64t + -64t + -16t2 + 16t2 Combine like terms: 190 + -190 = 0 -190 + -64t + 16t2 = 0 + 64t + -64t + -16t2 + 16t2 -190 + -64t + 16t2 = 64t + -64t + -16t2 + 16t2 Combine like terms: 64t + -64t = 0 -190 + -64t + 16t2 = 0 + -16t2 + 16t2 -190 + -64t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -190 + -64t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-95 + -32t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-95 + -32t + 8t2)' equal to zero and attempt to solve: Simplifying -95 + -32t + 8t2 = 0 Solving -95 + -32t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -11.875 + -4t + t2 = 0 Move the constant term to the right: Add '11.875' to each side of the equation. -11.875 + -4t + 11.875 + t2 = 0 + 11.875 Reorder the terms: -11.875 + 11.875 + -4t + t2 = 0 + 11.875 Combine like terms: -11.875 + 11.875 = 0.000 0.000 + -4t + t2 = 0 + 11.875 -4t + t2 = 0 + 11.875 Combine like terms: 0 + 11.875 = 11.875 -4t + t2 = 11.875 The t term is -4t. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4t + 4 + t2 = 11.875 + 4 Reorder the terms: 4 + -4t + t2 = 11.875 + 4 Combine like terms: 11.875 + 4 = 15.875 4 + -4t + t2 = 15.875 Factor a perfect square on the left side: (t + -2)(t + -2) = 15.875 Calculate the square root of the right side: 3.984344363 Break this problem into two subproblems by setting (t + -2) equal to 3.984344363 and -3.984344363.Subproblem 1
t + -2 = 3.984344363 Simplifying t + -2 = 3.984344363 Reorder the terms: -2 + t = 3.984344363 Solving -2 + t = 3.984344363 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 3.984344363 + 2 Combine like terms: -2 + 2 = 0 0 + t = 3.984344363 + 2 t = 3.984344363 + 2 Combine like terms: 3.984344363 + 2 = 5.984344363 t = 5.984344363 Simplifying t = 5.984344363Subproblem 2
t + -2 = -3.984344363 Simplifying t + -2 = -3.984344363 Reorder the terms: -2 + t = -3.984344363 Solving -2 + t = -3.984344363 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -3.984344363 + 2 Combine like terms: -2 + 2 = 0 0 + t = -3.984344363 + 2 t = -3.984344363 + 2 Combine like terms: -3.984344363 + 2 = -1.984344363 t = -1.984344363 Simplifying t = -1.984344363Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.984344363, -1.984344363}Solution
t = {5.984344363, -1.984344363}
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