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Simplifying 0 = (-1t2) + 7t + 10 Reorder the terms: 0 = 10 + 7t + (-1t2) Solving 0 = 10 + 7t + (-1t2) Solving for variable 't'. 0 + -10 + -7t + t2 = 10 + 7t + (-1t2) + -10 + -7t + (t2) Combine like terms: 0 + -10 = -10 -10 + -7t + t2 = 10 + 7t + (-1t2) + -10 + -7t + (t2) -10 + -7t + t2 = 10 + 7t + (-1t2) + -10 + -7t + t2 Reorder the terms: -10 + -7t + t2 = 10 + -10 + 7t + -7t + (-1t2) + t2 Combine like terms: 10 + -10 = 0 -10 + -7t + t2 = 0 + 7t + -7t + (-1t2) + t2 -10 + -7t + t2 = 7t + -7t + (-1t2) + t2 Combine like terms: 7t + -7t = 0 -10 + -7t + t2 = 0 + (-1t2) + t2 -10 + -7t + t2 = (-1t2) + t2 Combine like terms: (-1t2) + t2 = 0 -10 + -7t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -7t + 10 + t2 = 0 + 10 Reorder the terms: -10 + 10 + -7t + t2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -7t + t2 = 0 + 10 -7t + t2 = 0 + 10 Combine like terms: 0 + 10 = 10 -7t + t2 = 10 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 = 10 + 12.25 Reorder the terms: 12.25 + -7t + t2 = 10 + 12.25 Combine like terms: 10 + 12.25 = 22.25 12.25 + -7t + t2 = 22.25 Factor a perfect square on the left side: (t + -3.5)(t + -3.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (t + -3.5) equal to 4.716990566 and -4.716990566.Subproblem 1
t + -3.5 = 4.716990566 Simplifying t + -3.5 = 4.716990566 Reorder the terms: -3.5 + t = 4.716990566 Solving -3.5 + t = 4.716990566 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 = 4.716990566 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = 4.716990566 + 3.5 t = 4.716990566 + 3.5 Combine like terms: 4.716990566 + 3.5 = 8.216990566 t = 8.216990566 Simplifying t = 8.216990566Subproblem 2
t + -3.5 = -4.716990566 Simplifying t + -3.5 = -4.716990566 Reorder the terms: -3.5 + t = -4.716990566 Solving -3.5 + t = -4.716990566 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 = -4.716990566 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = -4.716990566 + 3.5 t = -4.716990566 + 3.5 Combine like terms: -4.716990566 + 3.5 = -1.216990566 t = -1.216990566 Simplifying t = -1.216990566Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.216990566, -1.216990566}
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