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Simplifying -5t2 + -2t + 32 = 0 Reorder the terms: 32 + -2t + -5t2 = 0 Solving 32 + -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'. -6.4 + 0.4t + t2 = 0 Move the constant term to the right: Add '6.4' to each side of the equation. -6.4 + 0.4t + 6.4 + t2 = 0 + 6.4 Reorder the terms: -6.4 + 6.4 + 0.4t + t2 = 0 + 6.4 Combine like terms: -6.4 + 6.4 = 0.0 0.0 + 0.4t + t2 = 0 + 6.4 0.4t + t2 = 0 + 6.4 Combine like terms: 0 + 6.4 = 6.4 0.4t + t2 = 6.4 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 = 6.4 + 0.04 Reorder the terms: 0.04 + 0.4t + t2 = 6.4 + 0.04 Combine like terms: 6.4 + 0.04 = 6.44 0.04 + 0.4t + t2 = 6.44 Factor a perfect square on the left side: (t + 0.2)(t + 0.2) = 6.44 Calculate the square root of the right side: 2.537715508 Break this problem into two subproblems by setting (t + 0.2) equal to 2.537715508 and -2.537715508.Subproblem 1
t + 0.2 = 2.537715508 Simplifying t + 0.2 = 2.537715508 Reorder the terms: 0.2 + t = 2.537715508 Solving 0.2 + t = 2.537715508 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 = 2.537715508 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + t = 2.537715508 + -0.2 t = 2.537715508 + -0.2 Combine like terms: 2.537715508 + -0.2 = 2.337715508 t = 2.337715508 Simplifying t = 2.337715508Subproblem 2
t + 0.2 = -2.537715508 Simplifying t + 0.2 = -2.537715508 Reorder the terms: 0.2 + t = -2.537715508 Solving 0.2 + t = -2.537715508 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 = -2.537715508 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + t = -2.537715508 + -0.2 t = -2.537715508 + -0.2 Combine like terms: -2.537715508 + -0.2 = -2.737715508 t = -2.737715508 Simplifying t = -2.737715508Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.337715508, -2.737715508}
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