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Simplifying 0 = -16t2 + 92t + 100 Reorder the terms: 0 = 100 + 92t + -16t2 Solving 0 = 100 + 92t + -16t2 Solving for variable 't'. Combine like terms: 0 + -100 = -100 -100 + -92t + 16t2 = 100 + 92t + -16t2 + -100 + -92t + 16t2 Reorder the terms: -100 + -92t + 16t2 = 100 + -100 + 92t + -92t + -16t2 + 16t2 Combine like terms: 100 + -100 = 0 -100 + -92t + 16t2 = 0 + 92t + -92t + -16t2 + 16t2 -100 + -92t + 16t2 = 92t + -92t + -16t2 + 16t2 Combine like terms: 92t + -92t = 0 -100 + -92t + 16t2 = 0 + -16t2 + 16t2 -100 + -92t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -100 + -92t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-25 + -23t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-25 + -23t + 4t2)' equal to zero and attempt to solve: Simplifying -25 + -23t + 4t2 = 0 Solving -25 + -23t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6.25 + -5.75t + t2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + -5.75t + 6.25 + t2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + -5.75t + t2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + -5.75t + t2 = 0 + 6.25 -5.75t + t2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 -5.75t + t2 = 6.25 The t term is -5.75t. Take half its coefficient (-2.875). Square it (8.265625) and add it to both sides. Add '8.265625' to each side of the equation. -5.75t + 8.265625 + t2 = 6.25 + 8.265625 Reorder the terms: 8.265625 + -5.75t + t2 = 6.25 + 8.265625 Combine like terms: 6.25 + 8.265625 = 14.515625 8.265625 + -5.75t + t2 = 14.515625 Factor a perfect square on the left side: (t + -2.875)(t + -2.875) = 14.515625 Calculate the square root of the right side: 3.809937664 Break this problem into two subproblems by setting (t + -2.875) equal to 3.809937664 and -3.809937664.Subproblem 1
t + -2.875 = 3.809937664 Simplifying t + -2.875 = 3.809937664 Reorder the terms: -2.875 + t = 3.809937664 Solving -2.875 + t = 3.809937664 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + t = 3.809937664 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + t = 3.809937664 + 2.875 t = 3.809937664 + 2.875 Combine like terms: 3.809937664 + 2.875 = 6.684937664 t = 6.684937664 Simplifying t = 6.684937664Subproblem 2
t + -2.875 = -3.809937664 Simplifying t + -2.875 = -3.809937664 Reorder the terms: -2.875 + t = -3.809937664 Solving -2.875 + t = -3.809937664 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + t = -3.809937664 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + t = -3.809937664 + 2.875 t = -3.809937664 + 2.875 Combine like terms: -3.809937664 + 2.875 = -0.934937664 t = -0.934937664 Simplifying t = -0.934937664Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.684937664, -0.934937664}Solution
t = {6.684937664, -0.934937664}
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