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Simplifying -4.9t2 + 5.1t + 1 = 0 Reorder the terms: 1 + 5.1t + -4.9t2 = 0 Solving 1 + 5.1t + -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'. -0.2040816327 + -1.040816327t + t2 = 0 Move the constant term to the right: Add '0.2040816327' to each side of the equation. -0.2040816327 + -1.040816327t + 0.2040816327 + t2 = 0 + 0.2040816327 Reorder the terms: -0.2040816327 + 0.2040816327 + -1.040816327t + t2 = 0 + 0.2040816327 Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000 0.0000000000 + -1.040816327t + t2 = 0 + 0.2040816327 -1.040816327t + t2 = 0 + 0.2040816327 Combine like terms: 0 + 0.2040816327 = 0.2040816327 -1.040816327t + t2 = 0.2040816327 The t term is -1.040816327t. Take half its coefficient (-0.5204081635). Square it (0.2708246566) and add it to both sides. Add '0.2708246566' to each side of the equation. -1.040816327t + 0.2708246566 + t2 = 0.2040816327 + 0.2708246566 Reorder the terms: 0.2708246566 + -1.040816327t + t2 = 0.2040816327 + 0.2708246566 Combine like terms: 0.2040816327 + 0.2708246566 = 0.4749062893 0.2708246566 + -1.040816327t + t2 = 0.4749062893 Factor a perfect square on the left side: (t + -0.5204081635)(t + -0.5204081635) = 0.4749062893 Calculate the square root of the right side: 0.689134449 Break this problem into two subproblems by setting (t + -0.5204081635) equal to 0.689134449 and -0.689134449.Subproblem 1
t + -0.5204081635 = 0.689134449 Simplifying t + -0.5204081635 = 0.689134449 Reorder the terms: -0.5204081635 + t = 0.689134449 Solving -0.5204081635 + t = 0.689134449 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5204081635' to each side of the equation. -0.5204081635 + 0.5204081635 + t = 0.689134449 + 0.5204081635 Combine like terms: -0.5204081635 + 0.5204081635 = 0.0000000000 0.0000000000 + t = 0.689134449 + 0.5204081635 t = 0.689134449 + 0.5204081635 Combine like terms: 0.689134449 + 0.5204081635 = 1.2095426125 t = 1.2095426125 Simplifying t = 1.2095426125Subproblem 2
t + -0.5204081635 = -0.689134449 Simplifying t + -0.5204081635 = -0.689134449 Reorder the terms: -0.5204081635 + t = -0.689134449 Solving -0.5204081635 + t = -0.689134449 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5204081635' to each side of the equation. -0.5204081635 + 0.5204081635 + t = -0.689134449 + 0.5204081635 Combine like terms: -0.5204081635 + 0.5204081635 = 0.0000000000 0.0000000000 + t = -0.689134449 + 0.5204081635 t = -0.689134449 + 0.5204081635 Combine like terms: -0.689134449 + 0.5204081635 = -0.1687262855 t = -0.1687262855 Simplifying t = -0.1687262855Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.2095426125, -0.1687262855}
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