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Simplifying 5t2 + 100t + 15 = 0 Reorder the terms: 15 + 100t + 5t2 = 0 Solving 15 + 100t + 5t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '5'. 5(3 + 20t + t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(3 + 20t + t2)' equal to zero and attempt to solve: Simplifying 3 + 20t + t2 = 0 Solving 3 + 20t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 20t + -3 + t2 = 0 + -3 Reorder the terms: 3 + -3 + 20t + t2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 20t + t2 = 0 + -3 20t + t2 = 0 + -3 Combine like terms: 0 + -3 = -3 20t + t2 = -3 The t term is 20t. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20t + 100 + t2 = -3 + 100 Reorder the terms: 100 + 20t + t2 = -3 + 100 Combine like terms: -3 + 100 = 97 100 + 20t + t2 = 97 Factor a perfect square on the left side: (t + 10)(t + 10) = 97 Calculate the square root of the right side: 9.848857802 Break this problem into two subproblems by setting (t + 10) equal to 9.848857802 and -9.848857802.Subproblem 1
t + 10 = 9.848857802 Simplifying t + 10 = 9.848857802 Reorder the terms: 10 + t = 9.848857802 Solving 10 + t = 9.848857802 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + t = 9.848857802 + -10 Combine like terms: 10 + -10 = 0 0 + t = 9.848857802 + -10 t = 9.848857802 + -10 Combine like terms: 9.848857802 + -10 = -0.151142198 t = -0.151142198 Simplifying t = -0.151142198Subproblem 2
t + 10 = -9.848857802 Simplifying t + 10 = -9.848857802 Reorder the terms: 10 + t = -9.848857802 Solving 10 + t = -9.848857802 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + t = -9.848857802 + -10 Combine like terms: 10 + -10 = 0 0 + t = -9.848857802 + -10 t = -9.848857802 + -10 Combine like terms: -9.848857802 + -10 = -19.848857802 t = -19.848857802 Simplifying t = -19.848857802Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.151142198, -19.848857802}Solution
t = {-0.151142198, -19.848857802}
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