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Simplifying 0 = -16t2 + 128t + 90 Reorder the terms: 0 = 90 + 128t + -16t2 Solving 0 = 90 + 128t + -16t2 Solving for variable 't'. Combine like terms: 0 + -90 = -90 -90 + -128t + 16t2 = 90 + 128t + -16t2 + -90 + -128t + 16t2 Reorder the terms: -90 + -128t + 16t2 = 90 + -90 + 128t + -128t + -16t2 + 16t2 Combine like terms: 90 + -90 = 0 -90 + -128t + 16t2 = 0 + 128t + -128t + -16t2 + 16t2 -90 + -128t + 16t2 = 128t + -128t + -16t2 + 16t2 Combine like terms: 128t + -128t = 0 -90 + -128t + 16t2 = 0 + -16t2 + 16t2 -90 + -128t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -90 + -128t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-45 + -64t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-45 + -64t + 8t2)' equal to zero and attempt to solve: Simplifying -45 + -64t + 8t2 = 0 Solving -45 + -64t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -5.625 + -8t + t2 = 0 Move the constant term to the right: Add '5.625' to each side of the equation. -5.625 + -8t + 5.625 + t2 = 0 + 5.625 Reorder the terms: -5.625 + 5.625 + -8t + t2 = 0 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + -8t + t2 = 0 + 5.625 -8t + t2 = 0 + 5.625 Combine like terms: 0 + 5.625 = 5.625 -8t + t2 = 5.625 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 = 5.625 + 16 Reorder the terms: 16 + -8t + t2 = 5.625 + 16 Combine like terms: 5.625 + 16 = 21.625 16 + -8t + t2 = 21.625 Factor a perfect square on the left side: (t + -4)(t + -4) = 21.625 Calculate the square root of the right side: 4.650268809 Break this problem into two subproblems by setting (t + -4) equal to 4.650268809 and -4.650268809.Subproblem 1
t + -4 = 4.650268809 Simplifying t + -4 = 4.650268809 Reorder the terms: -4 + t = 4.650268809 Solving -4 + t = 4.650268809 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 = 4.650268809 + 4 Combine like terms: -4 + 4 = 0 0 + t = 4.650268809 + 4 t = 4.650268809 + 4 Combine like terms: 4.650268809 + 4 = 8.650268809 t = 8.650268809 Simplifying t = 8.650268809Subproblem 2
t + -4 = -4.650268809 Simplifying t + -4 = -4.650268809 Reorder the terms: -4 + t = -4.650268809 Solving -4 + t = -4.650268809 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 = -4.650268809 + 4 Combine like terms: -4 + 4 = 0 0 + t = -4.650268809 + 4 t = -4.650268809 + 4 Combine like terms: -4.650268809 + 4 = -0.650268809 t = -0.650268809 Simplifying t = -0.650268809Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.650268809, -0.650268809}Solution
t = {8.650268809, -0.650268809}
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