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Simplifying -16t2 + 400t + 40 = 0 Reorder the terms: 40 + 400t + -16t2 = 0 Solving 40 + 400t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '8'. 8(5 + 50t + -2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(5 + 50t + -2t2)' equal to zero and attempt to solve: Simplifying 5 + 50t + -2t2 = 0 Solving 5 + 50t + -2t2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -2.5 + -25t + t2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -25t + 2.5 + t2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -25t + t2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -25t + t2 = 0 + 2.5 -25t + t2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -25t + t2 = 2.5 The t term is -25t. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25t + 156.25 + t2 = 2.5 + 156.25 Reorder the terms: 156.25 + -25t + t2 = 2.5 + 156.25 Combine like terms: 2.5 + 156.25 = 158.75 156.25 + -25t + t2 = 158.75 Factor a perfect square on the left side: (t + -12.5)(t + -12.5) = 158.75 Calculate the square root of the right side: 12.599603168 Break this problem into two subproblems by setting (t + -12.5) equal to 12.599603168 and -12.599603168.Subproblem 1
t + -12.5 = 12.599603168 Simplifying t + -12.5 = 12.599603168 Reorder the terms: -12.5 + t = 12.599603168 Solving -12.5 + t = 12.599603168 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + t = 12.599603168 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + t = 12.599603168 + 12.5 t = 12.599603168 + 12.5 Combine like terms: 12.599603168 + 12.5 = 25.099603168 t = 25.099603168 Simplifying t = 25.099603168Subproblem 2
t + -12.5 = -12.599603168 Simplifying t + -12.5 = -12.599603168 Reorder the terms: -12.5 + t = -12.599603168 Solving -12.5 + t = -12.599603168 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + t = -12.599603168 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + t = -12.599603168 + 12.5 t = -12.599603168 + 12.5 Combine like terms: -12.599603168 + 12.5 = -0.099603168 t = -0.099603168 Simplifying t = -0.099603168Solution
The solution to the problem is based on the solutions from the subproblems. t = {25.099603168, -0.099603168}Solution
t = {25.099603168, -0.099603168}
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