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Simplifying 0 = -4.9t * t + 28t + 1.2 Multiply t * t 0 = -4.9t2 + 28t + 1.2 Reorder the terms: 0 = 1.2 + 28t + -4.9t2 Solving 0 = 1.2 + 28t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -1.2 = -1.2 -1.2 + -28t + 4.9t2 = 1.2 + 28t + -4.9t2 + -1.2 + -28t + 4.9t2 Reorder the terms: -1.2 + -28t + 4.9t2 = 1.2 + -1.2 + 28t + -28t + -4.9t2 + 4.9t2 Combine like terms: 1.2 + -1.2 = 0.0 -1.2 + -28t + 4.9t2 = 0.0 + 28t + -28t + -4.9t2 + 4.9t2 -1.2 + -28t + 4.9t2 = 28t + -28t + -4.9t2 + 4.9t2 Combine like terms: 28t + -28t = 0 -1.2 + -28t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -1.2 + -28t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -1.2 + -28t + 4.9t2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -0.2448979592 + -5.714285714t + t2 = 0 Move the constant term to the right: Add '0.2448979592' to each side of the equation. -0.2448979592 + -5.714285714t + 0.2448979592 + t2 = 0 + 0.2448979592 Reorder the terms: -0.2448979592 + 0.2448979592 + -5.714285714t + t2 = 0 + 0.2448979592 Combine like terms: -0.2448979592 + 0.2448979592 = 0.0000000000 0.0000000000 + -5.714285714t + t2 = 0 + 0.2448979592 -5.714285714t + t2 = 0 + 0.2448979592 Combine like terms: 0 + 0.2448979592 = 0.2448979592 -5.714285714t + t2 = 0.2448979592 The t term is -5.714285714t. Take half its coefficient (-2.857142857). Square it (8.163265305) and add it to both sides. Add '8.163265305' to each side of the equation. -5.714285714t + 8.163265305 + t2 = 0.2448979592 + 8.163265305 Reorder the terms: 8.163265305 + -5.714285714t + t2 = 0.2448979592 + 8.163265305 Combine like terms: 0.2448979592 + 8.163265305 = 8.4081632642 8.163265305 + -5.714285714t + t2 = 8.4081632642 Factor a perfect square on the left side: (t + -2.857142857)(t + -2.857142857) = 8.4081632642 Calculate the square root of the right side: 2.899683304 Break this problem into two subproblems by setting (t + -2.857142857) equal to 2.899683304 and -2.899683304.Subproblem 1
t + -2.857142857 = 2.899683304 Simplifying t + -2.857142857 = 2.899683304 Reorder the terms: -2.857142857 + t = 2.899683304 Solving -2.857142857 + t = 2.899683304 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.857142857' to each side of the equation. -2.857142857 + 2.857142857 + t = 2.899683304 + 2.857142857 Combine like terms: -2.857142857 + 2.857142857 = 0.000000000 0.000000000 + t = 2.899683304 + 2.857142857 t = 2.899683304 + 2.857142857 Combine like terms: 2.899683304 + 2.857142857 = 5.756826161 t = 5.756826161 Simplifying t = 5.756826161Subproblem 2
t + -2.857142857 = -2.899683304 Simplifying t + -2.857142857 = -2.899683304 Reorder the terms: -2.857142857 + t = -2.899683304 Solving -2.857142857 + t = -2.899683304 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.857142857' to each side of the equation. -2.857142857 + 2.857142857 + t = -2.899683304 + 2.857142857 Combine like terms: -2.857142857 + 2.857142857 = 0.000000000 0.000000000 + t = -2.899683304 + 2.857142857 t = -2.899683304 + 2.857142857 Combine like terms: -2.899683304 + 2.857142857 = -0.042540447 t = -0.042540447 Simplifying t = -0.042540447Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.756826161, -0.042540447}
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