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Simplifying -5t2 + 4t + 2 = 0 Reorder the terms: 2 + 4t + -5t2 = 0 Solving 2 + 4t + -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'. -0.4 + -0.8t + t2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -0.8t + 0.4 + t2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -0.8t + t2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -0.8t + t2 = 0 + 0.4 -0.8t + t2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -0.8t + t2 = 0.4 The t term is -0.8t. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8t + 0.16 + t2 = 0.4 + 0.16 Reorder the terms: 0.16 + -0.8t + t2 = 0.4 + 0.16 Combine like terms: 0.4 + 0.16 = 0.56 0.16 + -0.8t + t2 = 0.56 Factor a perfect square on the left side: (t + -0.4)(t + -0.4) = 0.56 Calculate the square root of the right side: 0.748331477 Break this problem into two subproblems by setting (t + -0.4) equal to 0.748331477 and -0.748331477.Subproblem 1
t + -0.4 = 0.748331477 Simplifying t + -0.4 = 0.748331477 Reorder the terms: -0.4 + t = 0.748331477 Solving -0.4 + t = 0.748331477 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + t = 0.748331477 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + t = 0.748331477 + 0.4 t = 0.748331477 + 0.4 Combine like terms: 0.748331477 + 0.4 = 1.148331477 t = 1.148331477 Simplifying t = 1.148331477Subproblem 2
t + -0.4 = -0.748331477 Simplifying t + -0.4 = -0.748331477 Reorder the terms: -0.4 + t = -0.748331477 Solving -0.4 + t = -0.748331477 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + t = -0.748331477 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + t = -0.748331477 + 0.4 t = -0.748331477 + 0.4 Combine like terms: -0.748331477 + 0.4 = -0.348331477 t = -0.348331477 Simplifying t = -0.348331477Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.148331477, -0.348331477}
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