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Simplifying t2 + 6t + -15 = 0 Reorder the terms: -15 + 6t + t2 = 0 Solving -15 + 6t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 6t + 15 + t2 = 0 + 15 Reorder the terms: -15 + 15 + 6t + t2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 6t + t2 = 0 + 15 6t + t2 = 0 + 15 Combine like terms: 0 + 15 = 15 6t + t2 = 15 The t term is 6t. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6t + 9 + t2 = 15 + 9 Reorder the terms: 9 + 6t + t2 = 15 + 9 Combine like terms: 15 + 9 = 24 9 + 6t + t2 = 24 Factor a perfect square on the left side: (t + 3)(t + 3) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (t + 3) equal to 4.898979486 and -4.898979486.Subproblem 1
t + 3 = 4.898979486 Simplifying t + 3 = 4.898979486 Reorder the terms: 3 + t = 4.898979486 Solving 3 + t = 4.898979486 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + t = 4.898979486 + -3 Combine like terms: 3 + -3 = 0 0 + t = 4.898979486 + -3 t = 4.898979486 + -3 Combine like terms: 4.898979486 + -3 = 1.898979486 t = 1.898979486 Simplifying t = 1.898979486Subproblem 2
t + 3 = -4.898979486 Simplifying t + 3 = -4.898979486 Reorder the terms: 3 + t = -4.898979486 Solving 3 + t = -4.898979486 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + t = -4.898979486 + -3 Combine like terms: 3 + -3 = 0 0 + t = -4.898979486 + -3 t = -4.898979486 + -3 Combine like terms: -4.898979486 + -3 = -7.898979486 t = -7.898979486 Simplifying t = -7.898979486Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.898979486, -7.898979486}
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