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Simplifying -16t2 + 204t + -100 = 0 Reorder the terms: -100 + 204t + -16t2 = 0 Solving -100 + 204t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(-25 + 51t + -4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-25 + 51t + -4t2)' equal to zero and attempt to solve: Simplifying -25 + 51t + -4t2 = 0 Solving -25 + 51t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 6.25 + -12.75t + t2 = 0 Move the constant term to the right: Add '-6.25' to each side of the equation. 6.25 + -12.75t + -6.25 + t2 = 0 + -6.25 Reorder the terms: 6.25 + -6.25 + -12.75t + t2 = 0 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + -12.75t + t2 = 0 + -6.25 -12.75t + t2 = 0 + -6.25 Combine like terms: 0 + -6.25 = -6.25 -12.75t + t2 = -6.25 The t term is -12.75t. Take half its coefficient (-6.375). Square it (40.640625) and add it to both sides. Add '40.640625' to each side of the equation. -12.75t + 40.640625 + t2 = -6.25 + 40.640625 Reorder the terms: 40.640625 + -12.75t + t2 = -6.25 + 40.640625 Combine like terms: -6.25 + 40.640625 = 34.390625 40.640625 + -12.75t + t2 = 34.390625 Factor a perfect square on the left side: (t + -6.375)(t + -6.375) = 34.390625 Calculate the square root of the right side: 5.864352053 Break this problem into two subproblems by setting (t + -6.375) equal to 5.864352053 and -5.864352053.Subproblem 1
t + -6.375 = 5.864352053 Simplifying t + -6.375 = 5.864352053 Reorder the terms: -6.375 + t = 5.864352053 Solving -6.375 + t = 5.864352053 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.375' to each side of the equation. -6.375 + 6.375 + t = 5.864352053 + 6.375 Combine like terms: -6.375 + 6.375 = 0.000 0.000 + t = 5.864352053 + 6.375 t = 5.864352053 + 6.375 Combine like terms: 5.864352053 + 6.375 = 12.239352053 t = 12.239352053 Simplifying t = 12.239352053Subproblem 2
t + -6.375 = -5.864352053 Simplifying t + -6.375 = -5.864352053 Reorder the terms: -6.375 + t = -5.864352053 Solving -6.375 + t = -5.864352053 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.375' to each side of the equation. -6.375 + 6.375 + t = -5.864352053 + 6.375 Combine like terms: -6.375 + 6.375 = 0.000 0.000 + t = -5.864352053 + 6.375 t = -5.864352053 + 6.375 Combine like terms: -5.864352053 + 6.375 = 0.510647947 t = 0.510647947 Simplifying t = 0.510647947Solution
The solution to the problem is based on the solutions from the subproblems. t = {12.239352053, 0.510647947}Solution
t = {12.239352053, 0.510647947}
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