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Simplifying -1t2 + 176t + 1536 = 0 Reorder the terms: 1536 + 176t + -1t2 = 0 Solving 1536 + 176t + -1t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1536 + -176t + t2 = 0 Move the constant term to the right: Add '1536' to each side of the equation. -1536 + -176t + 1536 + t2 = 0 + 1536 Reorder the terms: -1536 + 1536 + -176t + t2 = 0 + 1536 Combine like terms: -1536 + 1536 = 0 0 + -176t + t2 = 0 + 1536 -176t + t2 = 0 + 1536 Combine like terms: 0 + 1536 = 1536 -176t + t2 = 1536 The t term is -176t. Take half its coefficient (-88). Square it (7744) and add it to both sides. Add '7744' to each side of the equation. -176t + 7744 + t2 = 1536 + 7744 Reorder the terms: 7744 + -176t + t2 = 1536 + 7744 Combine like terms: 1536 + 7744 = 9280 7744 + -176t + t2 = 9280 Factor a perfect square on the left side: (t + -88)(t + -88) = 9280 Calculate the square root of the right side: 96.33275663 Break this problem into two subproblems by setting (t + -88) equal to 96.33275663 and -96.33275663.Subproblem 1
t + -88 = 96.33275663 Simplifying t + -88 = 96.33275663 Reorder the terms: -88 + t = 96.33275663 Solving -88 + t = 96.33275663 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '88' to each side of the equation. -88 + 88 + t = 96.33275663 + 88 Combine like terms: -88 + 88 = 0 0 + t = 96.33275663 + 88 t = 96.33275663 + 88 Combine like terms: 96.33275663 + 88 = 184.33275663 t = 184.33275663 Simplifying t = 184.33275663Subproblem 2
t + -88 = -96.33275663 Simplifying t + -88 = -96.33275663 Reorder the terms: -88 + t = -96.33275663 Solving -88 + t = -96.33275663 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '88' to each side of the equation. -88 + 88 + t = -96.33275663 + 88 Combine like terms: -88 + 88 = 0 0 + t = -96.33275663 + 88 t = -96.33275663 + 88 Combine like terms: -96.33275663 + 88 = -8.33275663 t = -8.33275663 Simplifying t = -8.33275663Solution
The solution to the problem is based on the solutions from the subproblems. t = {184.33275663, -8.33275663}
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