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Simplifying 10 + 2t + -5t2 = 0 Solving 10 + 2t + -5t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -2 + -0.4t + t2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -0.4t + 2 + t2 = 0 + 2 Reorder the terms: -2 + 2 + -0.4t + t2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -0.4t + t2 = 0 + 2 -0.4t + t2 = 0 + 2 Combine like terms: 0 + 2 = 2 -0.4t + t2 = 2 The t term is -0.4t. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4t + 0.04 + t2 = 2 + 0.04 Reorder the terms: 0.04 + -0.4t + t2 = 2 + 0.04 Combine like terms: 2 + 0.04 = 2.04 0.04 + -0.4t + t2 = 2.04 Factor a perfect square on the left side: (t + -0.2)(t + -0.2) = 2.04 Calculate the square root of the right side: 1.428285686 Break this problem into two subproblems by setting (t + -0.2) equal to 1.428285686 and -1.428285686.Subproblem 1
t + -0.2 = 1.428285686 Simplifying t + -0.2 = 1.428285686 Reorder the terms: -0.2 + t = 1.428285686 Solving -0.2 + t = 1.428285686 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + t = 1.428285686 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + t = 1.428285686 + 0.2 t = 1.428285686 + 0.2 Combine like terms: 1.428285686 + 0.2 = 1.628285686 t = 1.628285686 Simplifying t = 1.628285686Subproblem 2
t + -0.2 = -1.428285686 Simplifying t + -0.2 = -1.428285686 Reorder the terms: -0.2 + t = -1.428285686 Solving -0.2 + t = -1.428285686 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + t = -1.428285686 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + t = -1.428285686 + 0.2 t = -1.428285686 + 0.2 Combine like terms: -1.428285686 + 0.2 = -1.228285686 t = -1.228285686 Simplifying t = -1.228285686Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.628285686, -1.228285686}
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