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Simplifying -4.9t2 + 4.9t + 0.83 = 0 Reorder the terms: 0.83 + 4.9t + -4.9t2 = 0 Solving 0.83 + 4.9t + -4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -0.1693877551 + -1t + t2 = 0 Move the constant term to the right: Add '0.1693877551' to each side of the equation. -0.1693877551 + -1t + 0.1693877551 + t2 = 0 + 0.1693877551 Reorder the terms: -0.1693877551 + 0.1693877551 + -1t + t2 = 0 + 0.1693877551 Combine like terms: -0.1693877551 + 0.1693877551 = 0.0000000000 0.0000000000 + -1t + t2 = 0 + 0.1693877551 -1t + t2 = 0 + 0.1693877551 Combine like terms: 0 + 0.1693877551 = 0.1693877551 -1t + t2 = 0.1693877551 The t term is -1t. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1t + 0.25 + t2 = 0.1693877551 + 0.25 Reorder the terms: 0.25 + -1t + t2 = 0.1693877551 + 0.25 Combine like terms: 0.1693877551 + 0.25 = 0.4193877551 0.25 + -1t + t2 = 0.4193877551 Factor a perfect square on the left side: (t + -0.5)(t + -0.5) = 0.4193877551 Calculate the square root of the right side: 0.64760154 Break this problem into two subproblems by setting (t + -0.5) equal to 0.64760154 and -0.64760154.Subproblem 1
t + -0.5 = 0.64760154 Simplifying t + -0.5 = 0.64760154 Reorder the terms: -0.5 + t = 0.64760154 Solving -0.5 + t = 0.64760154 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = 0.64760154 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = 0.64760154 + 0.5 t = 0.64760154 + 0.5 Combine like terms: 0.64760154 + 0.5 = 1.14760154 t = 1.14760154 Simplifying t = 1.14760154Subproblem 2
t + -0.5 = -0.64760154 Simplifying t + -0.5 = -0.64760154 Reorder the terms: -0.5 + t = -0.64760154 Solving -0.5 + t = -0.64760154 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = -0.64760154 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = -0.64760154 + 0.5 t = -0.64760154 + 0.5 Combine like terms: -0.64760154 + 0.5 = -0.14760154 t = -0.14760154 Simplifying t = -0.14760154Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.14760154, -0.14760154}
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