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Simplifying t2 + 15t + -39 = 0 Reorder the terms: -39 + 15t + t2 = 0 Solving -39 + 15t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '39' to each side of the equation. -39 + 15t + 39 + t2 = 0 + 39 Reorder the terms: -39 + 39 + 15t + t2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + 15t + t2 = 0 + 39 15t + t2 = 0 + 39 Combine like terms: 0 + 39 = 39 15t + t2 = 39 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 = 39 + 56.25 Reorder the terms: 56.25 + 15t + t2 = 39 + 56.25 Combine like terms: 39 + 56.25 = 95.25 56.25 + 15t + t2 = 95.25 Factor a perfect square on the left side: (t + 7.5)(t + 7.5) = 95.25 Calculate the square root of the right side: 9.759610648 Break this problem into two subproblems by setting (t + 7.5) equal to 9.759610648 and -9.759610648.Subproblem 1
t + 7.5 = 9.759610648 Simplifying t + 7.5 = 9.759610648 Reorder the terms: 7.5 + t = 9.759610648 Solving 7.5 + t = 9.759610648 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 = 9.759610648 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + t = 9.759610648 + -7.5 t = 9.759610648 + -7.5 Combine like terms: 9.759610648 + -7.5 = 2.259610648 t = 2.259610648 Simplifying t = 2.259610648Subproblem 2
t + 7.5 = -9.759610648 Simplifying t + 7.5 = -9.759610648 Reorder the terms: 7.5 + t = -9.759610648 Solving 7.5 + t = -9.759610648 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 = -9.759610648 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + t = -9.759610648 + -7.5 t = -9.759610648 + -7.5 Combine like terms: -9.759610648 + -7.5 = -17.259610648 t = -17.259610648 Simplifying t = -17.259610648Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.259610648, -17.259610648}
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