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Simplifying -4.9t2 + 4.9t + 0.8 = 1.829 Reorder the terms: 0.8 + 4.9t + -4.9t2 = 1.829 Solving 0.8 + 4.9t + -4.9t2 = 1.829 Solving for variable 't'. Reorder the terms: 0.8 + -1.829 + 4.9t + -4.9t2 = 1.829 + -1.829 Combine like terms: 0.8 + -1.829 = -1.029 -1.029 + 4.9t + -4.9t2 = 1.829 + -1.829 Combine like terms: 1.829 + -1.829 = 0.000 -1.029 + 4.9t + -4.9t2 = 0.000 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. 0.21 + -1t + t2 = 0.00 Move the constant term to the right: Add '-0.21' to each side of the equation. 0.21 + -1t + -0.21 + t2 = 0.00 + -0.21 Reorder the terms: 0.21 + -0.21 + -1t + t2 = 0.00 + -0.21 Combine like terms: 0.21 + -0.21 = 0.00 0.00 + -1t + t2 = 0.00 + -0.21 -1t + t2 = 0.00 + -0.21 Combine like terms: 0.00 + -0.21 = -0.21 -1t + t2 = -0.21 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 = -0.21 + 0.25 Reorder the terms: 0.25 + -1t + t2 = -0.21 + 0.25 Combine like terms: -0.21 + 0.25 = 0.04 0.25 + -1t + t2 = 0.04 Factor a perfect square on the left side: (t + -0.5)(t + -0.5) = 0.04 Calculate the square root of the right side: 0.2 Break this problem into two subproblems by setting (t + -0.5) equal to 0.2 and -0.2.Subproblem 1
t + -0.5 = 0.2 Simplifying t + -0.5 = 0.2 Reorder the terms: -0.5 + t = 0.2 Solving -0.5 + t = 0.2 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 = 0.2 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = 0.2 + 0.5 t = 0.2 + 0.5 Combine like terms: 0.2 + 0.5 = 0.7 t = 0.7 Simplifying t = 0.7Subproblem 2
t + -0.5 = -0.2 Simplifying t + -0.5 = -0.2 Reorder the terms: -0.5 + t = -0.2 Solving -0.5 + t = -0.2 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 = -0.2 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = -0.2 + 0.5 t = -0.2 + 0.5 Combine like terms: -0.2 + 0.5 = 0.3 t = 0.3 Simplifying t = 0.3Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.7, 0.3}
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