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Simplifying 4.9(t2) + -10.5t + -63 = 0 Reorder the terms: -63 + -10.5t + 4.9t2 = 0 Solving -63 + -10.5t + 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'. -12.85714286 + -2.142857143t + t2 = 0 Move the constant term to the right: Add '12.85714286' to each side of the equation. -12.85714286 + -2.142857143t + 12.85714286 + t2 = 0 + 12.85714286 Reorder the terms: -12.85714286 + 12.85714286 + -2.142857143t + t2 = 0 + 12.85714286 Combine like terms: -12.85714286 + 12.85714286 = 0.00000000 0.00000000 + -2.142857143t + t2 = 0 + 12.85714286 -2.142857143t + t2 = 0 + 12.85714286 Combine like terms: 0 + 12.85714286 = 12.85714286 -2.142857143t + t2 = 12.85714286 The t term is -2.142857143t. Take half its coefficient (-1.071428572). Square it (1.147959185) and add it to both sides. Add '1.147959185' to each side of the equation. -2.142857143t + 1.147959185 + t2 = 12.85714286 + 1.147959185 Reorder the terms: 1.147959185 + -2.142857143t + t2 = 12.85714286 + 1.147959185 Combine like terms: 12.85714286 + 1.147959185 = 14.005102045 1.147959185 + -2.142857143t + t2 = 14.005102045 Factor a perfect square on the left side: (t + -1.071428572)(t + -1.071428572) = 14.005102045 Calculate the square root of the right side: 3.742339114 Break this problem into two subproblems by setting (t + -1.071428572) equal to 3.742339114 and -3.742339114.Subproblem 1
t + -1.071428572 = 3.742339114 Simplifying t + -1.071428572 = 3.742339114 Reorder the terms: -1.071428572 + t = 3.742339114 Solving -1.071428572 + t = 3.742339114 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.071428572' to each side of the equation. -1.071428572 + 1.071428572 + t = 3.742339114 + 1.071428572 Combine like terms: -1.071428572 + 1.071428572 = 0.000000000 0.000000000 + t = 3.742339114 + 1.071428572 t = 3.742339114 + 1.071428572 Combine like terms: 3.742339114 + 1.071428572 = 4.813767686 t = 4.813767686 Simplifying t = 4.813767686Subproblem 2
t + -1.071428572 = -3.742339114 Simplifying t + -1.071428572 = -3.742339114 Reorder the terms: -1.071428572 + t = -3.742339114 Solving -1.071428572 + t = -3.742339114 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.071428572' to each side of the equation. -1.071428572 + 1.071428572 + t = -3.742339114 + 1.071428572 Combine like terms: -1.071428572 + 1.071428572 = 0.000000000 0.000000000 + t = -3.742339114 + 1.071428572 t = -3.742339114 + 1.071428572 Combine like terms: -3.742339114 + 1.071428572 = -2.670910542 t = -2.670910542 Simplifying t = -2.670910542Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.813767686, -2.670910542}
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