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Simplifying 15 = t2 + -8t Reorder the terms: 15 = -8t + t2 Solving 15 = -8t + t2 Solving for variable 't'. Reorder the terms: 15 + 8t + -1t2 = -8t + 8t + t2 + -1t2 Combine like terms: -8t + 8t = 0 15 + 8t + -1t2 = 0 + t2 + -1t2 15 + 8t + -1t2 = t2 + -1t2 Combine like terms: t2 + -1t2 = 0 15 + 8t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -15 + -8t + t2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + -8t + 15 + t2 = 0 + 15 Reorder the terms: -15 + 15 + -8t + t2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -8t + t2 = 0 + 15 -8t + t2 = 0 + 15 Combine like terms: 0 + 15 = 15 -8t + t2 = 15 The t term is -8t. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8t + 16 + t2 = 15 + 16 Reorder the terms: 16 + -8t + t2 = 15 + 16 Combine like terms: 15 + 16 = 31 16 + -8t + t2 = 31 Factor a perfect square on the left side: (t + -4)(t + -4) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (t + -4) equal to 5.567764363 and -5.567764363.Subproblem 1
t + -4 = 5.567764363 Simplifying t + -4 = 5.567764363 Reorder the terms: -4 + t = 5.567764363 Solving -4 + t = 5.567764363 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = 5.567764363 + 4 Combine like terms: -4 + 4 = 0 0 + t = 5.567764363 + 4 t = 5.567764363 + 4 Combine like terms: 5.567764363 + 4 = 9.567764363 t = 9.567764363 Simplifying t = 9.567764363Subproblem 2
t + -4 = -5.567764363 Simplifying t + -4 = -5.567764363 Reorder the terms: -4 + t = -5.567764363 Solving -4 + t = -5.567764363 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = -5.567764363 + 4 Combine like terms: -4 + 4 = 0 0 + t = -5.567764363 + 4 t = -5.567764363 + 4 Combine like terms: -5.567764363 + 4 = -1.567764363 t = -1.567764363 Simplifying t = -1.567764363Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.567764363, -1.567764363}
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