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Simplifying (8 + -7t) + -1(t2 + -1) = 0 Remove parenthesis around (8 + -7t) 8 + -7t + -1(t2 + -1) = 0 Reorder the terms: 8 + -7t + -1(-1 + t2) = 0 8 + -7t + (-1 * -1 + t2 * -1) = 0 8 + -7t + (1 + -1t2) = 0 Reorder the terms: 8 + 1 + -7t + -1t2 = 0 Combine like terms: 8 + 1 = 9 9 + -7t + -1t2 = 0 Solving 9 + -7t + -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'. -9 + 7t + t2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 7t + 9 + t2 = 0 + 9 Reorder the terms: -9 + 9 + 7t + t2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 7t + t2 = 0 + 9 7t + t2 = 0 + 9 Combine like terms: 0 + 9 = 9 7t + t2 = 9 The t term is 7t. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7t + 12.25 + t2 = 9 + 12.25 Reorder the terms: 12.25 + 7t + t2 = 9 + 12.25 Combine like terms: 9 + 12.25 = 21.25 12.25 + 7t + t2 = 21.25 Factor a perfect square on the left side: (t + 3.5)(t + 3.5) = 21.25 Calculate the square root of the right side: 4.609772229 Break this problem into two subproblems by setting (t + 3.5) equal to 4.609772229 and -4.609772229.Subproblem 1
t + 3.5 = 4.609772229 Simplifying t + 3.5 = 4.609772229 Reorder the terms: 3.5 + t = 4.609772229 Solving 3.5 + t = 4.609772229 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + t = 4.609772229 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + t = 4.609772229 + -3.5 t = 4.609772229 + -3.5 Combine like terms: 4.609772229 + -3.5 = 1.109772229 t = 1.109772229 Simplifying t = 1.109772229Subproblem 2
t + 3.5 = -4.609772229 Simplifying t + 3.5 = -4.609772229 Reorder the terms: 3.5 + t = -4.609772229 Solving 3.5 + t = -4.609772229 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + t = -4.609772229 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + t = -4.609772229 + -3.5 t = -4.609772229 + -3.5 Combine like terms: -4.609772229 + -3.5 = -8.109772229 t = -8.109772229 Simplifying t = -8.109772229Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.109772229, -8.109772229}
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