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Simplifying t2 + 8t + -6520 = 0 Reorder the terms: -6520 + 8t + t2 = 0 Solving -6520 + 8t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '6520' to each side of the equation. -6520 + 8t + 6520 + t2 = 0 + 6520 Reorder the terms: -6520 + 6520 + 8t + t2 = 0 + 6520 Combine like terms: -6520 + 6520 = 0 0 + 8t + t2 = 0 + 6520 8t + t2 = 0 + 6520 Combine like terms: 0 + 6520 = 6520 8t + t2 = 6520 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 = 6520 + 16 Reorder the terms: 16 + 8t + t2 = 6520 + 16 Combine like terms: 6520 + 16 = 6536 16 + 8t + t2 = 6536 Factor a perfect square on the left side: (t + 4)(t + 4) = 6536 Calculate the square root of the right side: 80.845531726 Break this problem into two subproblems by setting (t + 4) equal to 80.845531726 and -80.845531726.Subproblem 1
t + 4 = 80.845531726 Simplifying t + 4 = 80.845531726 Reorder the terms: 4 + t = 80.845531726 Solving 4 + t = 80.845531726 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 = 80.845531726 + -4 Combine like terms: 4 + -4 = 0 0 + t = 80.845531726 + -4 t = 80.845531726 + -4 Combine like terms: 80.845531726 + -4 = 76.845531726 t = 76.845531726 Simplifying t = 76.845531726Subproblem 2
t + 4 = -80.845531726 Simplifying t + 4 = -80.845531726 Reorder the terms: 4 + t = -80.845531726 Solving 4 + t = -80.845531726 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 = -80.845531726 + -4 Combine like terms: 4 + -4 = 0 0 + t = -80.845531726 + -4 t = -80.845531726 + -4 Combine like terms: -80.845531726 + -4 = -84.845531726 t = -84.845531726 Simplifying t = -84.845531726Solution
The solution to the problem is based on the solutions from the subproblems. t = {76.845531726, -84.845531726}
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