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Simplifying 5t2 + -65t + 30 = 0 Reorder the terms: 30 + -65t + 5t2 = 0 Solving 30 + -65t + 5t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '5'. 5(6 + -13t + t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(6 + -13t + t2)' equal to zero and attempt to solve: Simplifying 6 + -13t + t2 = 0 Solving 6 + -13t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -13t + -6 + t2 = 0 + -6 Reorder the terms: 6 + -6 + -13t + t2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -13t + t2 = 0 + -6 -13t + t2 = 0 + -6 Combine like terms: 0 + -6 = -6 -13t + t2 = -6 The t term is -13t. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13t + 42.25 + t2 = -6 + 42.25 Reorder the terms: 42.25 + -13t + t2 = -6 + 42.25 Combine like terms: -6 + 42.25 = 36.25 42.25 + -13t + t2 = 36.25 Factor a perfect square on the left side: (t + -6.5)(t + -6.5) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting (t + -6.5) equal to 6.020797289 and -6.020797289.Subproblem 1
t + -6.5 = 6.020797289 Simplifying t + -6.5 = 6.020797289 Reorder the terms: -6.5 + t = 6.020797289 Solving -6.5 + t = 6.020797289 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + t = 6.020797289 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + t = 6.020797289 + 6.5 t = 6.020797289 + 6.5 Combine like terms: 6.020797289 + 6.5 = 12.520797289 t = 12.520797289 Simplifying t = 12.520797289Subproblem 2
t + -6.5 = -6.020797289 Simplifying t + -6.5 = -6.020797289 Reorder the terms: -6.5 + t = -6.020797289 Solving -6.5 + t = -6.020797289 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + t = -6.020797289 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + t = -6.020797289 + 6.5 t = -6.020797289 + 6.5 Combine like terms: -6.020797289 + 6.5 = 0.479202711 t = 0.479202711 Simplifying t = 0.479202711Solution
The solution to the problem is based on the solutions from the subproblems. t = {12.520797289, 0.479202711}Solution
t = {12.520797289, 0.479202711}
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