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Simplifying t2 + 15t + 13 = 0 Reorder the terms: 13 + 15t + t2 = 0 Solving 13 + 15t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + 15t + -13 + t2 = 0 + -13 Reorder the terms: 13 + -13 + 15t + t2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 15t + t2 = 0 + -13 15t + t2 = 0 + -13 Combine like terms: 0 + -13 = -13 15t + t2 = -13 The t term is 15t. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15t + 56.25 + t2 = -13 + 56.25 Reorder the terms: 56.25 + 15t + t2 = -13 + 56.25 Combine like terms: -13 + 56.25 = 43.25 56.25 + 15t + t2 = 43.25 Factor a perfect square on the left side: (t + 7.5)(t + 7.5) = 43.25 Calculate the square root of the right side: 6.576473219 Break this problem into two subproblems by setting (t + 7.5) equal to 6.576473219 and -6.576473219.Subproblem 1
t + 7.5 = 6.576473219 Simplifying t + 7.5 = 6.576473219 Reorder the terms: 7.5 + t = 6.576473219 Solving 7.5 + t = 6.576473219 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + t = 6.576473219 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + t = 6.576473219 + -7.5 t = 6.576473219 + -7.5 Combine like terms: 6.576473219 + -7.5 = -0.923526781 t = -0.923526781 Simplifying t = -0.923526781Subproblem 2
t + 7.5 = -6.576473219 Simplifying t + 7.5 = -6.576473219 Reorder the terms: 7.5 + t = -6.576473219 Solving 7.5 + t = -6.576473219 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + t = -6.576473219 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + t = -6.576473219 + -7.5 t = -6.576473219 + -7.5 Combine like terms: -6.576473219 + -7.5 = -14.076473219 t = -14.076473219 Simplifying t = -14.076473219Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.923526781, -14.076473219}
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