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Simplifying -4.9t2 + 12.25t + -6.664 = 0 Reorder the terms: -6.664 + 12.25t + -4.9t2 = 0 Solving -6.664 + 12.25t + -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'. 1.36 + -2.5t + t2 = 0 Move the constant term to the right: Add '-1.36' to each side of the equation. 1.36 + -2.5t + -1.36 + t2 = 0 + -1.36 Reorder the terms: 1.36 + -1.36 + -2.5t + t2 = 0 + -1.36 Combine like terms: 1.36 + -1.36 = 0.00 0.00 + -2.5t + t2 = 0 + -1.36 -2.5t + t2 = 0 + -1.36 Combine like terms: 0 + -1.36 = -1.36 -2.5t + t2 = -1.36 The t term is -2.5t. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5t + 1.5625 + t2 = -1.36 + 1.5625 Reorder the terms: 1.5625 + -2.5t + t2 = -1.36 + 1.5625 Combine like terms: -1.36 + 1.5625 = 0.2025 1.5625 + -2.5t + t2 = 0.2025 Factor a perfect square on the left side: (t + -1.25)(t + -1.25) = 0.2025 Calculate the square root of the right side: 0.45 Break this problem into two subproblems by setting (t + -1.25) equal to 0.45 and -0.45.Subproblem 1
t + -1.25 = 0.45 Simplifying t + -1.25 = 0.45 Reorder the terms: -1.25 + t = 0.45 Solving -1.25 + t = 0.45 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + t = 0.45 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + t = 0.45 + 1.25 t = 0.45 + 1.25 Combine like terms: 0.45 + 1.25 = 1.7 t = 1.7 Simplifying t = 1.7Subproblem 2
t + -1.25 = -0.45 Simplifying t + -1.25 = -0.45 Reorder the terms: -1.25 + t = -0.45 Solving -1.25 + t = -0.45 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + t = -0.45 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + t = -0.45 + 1.25 t = -0.45 + 1.25 Combine like terms: -0.45 + 1.25 = 0.8 t = 0.8 Simplifying t = 0.8Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.7, 0.8}
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