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Simplifying -4.9t2 + 3t + 1.4 = 0 Reorder the terms: 1.4 + 3t + -4.9t2 = 0 Solving 1.4 + 3t + -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'. -0.2857142857 + -0.612244898t + t2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + -0.612244898t + 0.2857142857 + t2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + -0.612244898t + t2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + -0.612244898t + t2 = 0 + 0.2857142857 -0.612244898t + t2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 -0.612244898t + t2 = 0.2857142857 The t term is -0.612244898t. Take half its coefficient (-0.306122449). Square it (0.09371095378) and add it to both sides. Add '0.09371095378' to each side of the equation. -0.612244898t + 0.09371095378 + t2 = 0.2857142857 + 0.09371095378 Reorder the terms: 0.09371095378 + -0.612244898t + t2 = 0.2857142857 + 0.09371095378 Combine like terms: 0.2857142857 + 0.09371095378 = 0.37942523948 0.09371095378 + -0.612244898t + t2 = 0.37942523948 Factor a perfect square on the left side: (t + -0.306122449)(t + -0.306122449) = 0.37942523948 Calculate the square root of the right side: 0.615975032 Break this problem into two subproblems by setting (t + -0.306122449) equal to 0.615975032 and -0.615975032.Subproblem 1
t + -0.306122449 = 0.615975032 Simplifying t + -0.306122449 = 0.615975032 Reorder the terms: -0.306122449 + t = 0.615975032 Solving -0.306122449 + t = 0.615975032 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.306122449' to each side of the equation. -0.306122449 + 0.306122449 + t = 0.615975032 + 0.306122449 Combine like terms: -0.306122449 + 0.306122449 = 0.000000000 0.000000000 + t = 0.615975032 + 0.306122449 t = 0.615975032 + 0.306122449 Combine like terms: 0.615975032 + 0.306122449 = 0.922097481 t = 0.922097481 Simplifying t = 0.922097481Subproblem 2
t + -0.306122449 = -0.615975032 Simplifying t + -0.306122449 = -0.615975032 Reorder the terms: -0.306122449 + t = -0.615975032 Solving -0.306122449 + t = -0.615975032 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.306122449' to each side of the equation. -0.306122449 + 0.306122449 + t = -0.615975032 + 0.306122449 Combine like terms: -0.306122449 + 0.306122449 = 0.000000000 0.000000000 + t = -0.615975032 + 0.306122449 t = -0.615975032 + 0.306122449 Combine like terms: -0.615975032 + 0.306122449 = -0.309852583 t = -0.309852583 Simplifying t = -0.309852583Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.922097481, -0.309852583}
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