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Simplifying 100t2 + 6600t + 11700 = 0 Reorder the terms: 11700 + 6600t + 100t2 = 0 Solving 11700 + 6600t + 100t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '100'. 100(117 + 66t + t2) = 0 Ignore the factor 100.Subproblem 1
Set the factor '(117 + 66t + t2)' equal to zero and attempt to solve: Simplifying 117 + 66t + t2 = 0 Solving 117 + 66t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-117' to each side of the equation. 117 + 66t + -117 + t2 = 0 + -117 Reorder the terms: 117 + -117 + 66t + t2 = 0 + -117 Combine like terms: 117 + -117 = 0 0 + 66t + t2 = 0 + -117 66t + t2 = 0 + -117 Combine like terms: 0 + -117 = -117 66t + t2 = -117 The t term is 66t. Take half its coefficient (33). Square it (1089) and add it to both sides. Add '1089' to each side of the equation. 66t + 1089 + t2 = -117 + 1089 Reorder the terms: 1089 + 66t + t2 = -117 + 1089 Combine like terms: -117 + 1089 = 972 1089 + 66t + t2 = 972 Factor a perfect square on the left side: (t + 33)(t + 33) = 972 Calculate the square root of the right side: 31.176914536 Break this problem into two subproblems by setting (t + 33) equal to 31.176914536 and -31.176914536.Subproblem 1
t + 33 = 31.176914536 Simplifying t + 33 = 31.176914536 Reorder the terms: 33 + t = 31.176914536 Solving 33 + t = 31.176914536 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-33' to each side of the equation. 33 + -33 + t = 31.176914536 + -33 Combine like terms: 33 + -33 = 0 0 + t = 31.176914536 + -33 t = 31.176914536 + -33 Combine like terms: 31.176914536 + -33 = -1.823085464 t = -1.823085464 Simplifying t = -1.823085464Subproblem 2
t + 33 = -31.176914536 Simplifying t + 33 = -31.176914536 Reorder the terms: 33 + t = -31.176914536 Solving 33 + t = -31.176914536 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-33' to each side of the equation. 33 + -33 + t = -31.176914536 + -33 Combine like terms: 33 + -33 = 0 0 + t = -31.176914536 + -33 t = -31.176914536 + -33 Combine like terms: -31.176914536 + -33 = -64.176914536 t = -64.176914536 Simplifying t = -64.176914536Solution
The solution to the problem is based on the solutions from the subproblems. t = {-1.823085464, -64.176914536}Solution
t = {-1.823085464, -64.176914536}
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