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Simplifying 7 = 12t + -4.9t2 Solving 7 = 12t + -4.9t2 Solving for variable 't'. Reorder the terms: 7 + -12t + 4.9t2 = 12t + -12t + -4.9t2 + 4.9t2 Combine like terms: 12t + -12t = 0 7 + -12t + 4.9t2 = 0 + -4.9t2 + 4.9t2 7 + -12t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 7 + -12t + 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'. 1.428571429 + -2.448979592t + t2 = 0 Move the constant term to the right: Add '-1.428571429' to each side of the equation. 1.428571429 + -2.448979592t + -1.428571429 + t2 = 0 + -1.428571429 Reorder the terms: 1.428571429 + -1.428571429 + -2.448979592t + t2 = 0 + -1.428571429 Combine like terms: 1.428571429 + -1.428571429 = 0.000000000 0.000000000 + -2.448979592t + t2 = 0 + -1.428571429 -2.448979592t + t2 = 0 + -1.428571429 Combine like terms: 0 + -1.428571429 = -1.428571429 -2.448979592t + t2 = -1.428571429 The t term is -2.448979592t. Take half its coefficient (-1.224489796). Square it (1.499375261) and add it to both sides. Add '1.499375261' to each side of the equation. -2.448979592t + 1.499375261 + t2 = -1.428571429 + 1.499375261 Reorder the terms: 1.499375261 + -2.448979592t + t2 = -1.428571429 + 1.499375261 Combine like terms: -1.428571429 + 1.499375261 = 0.070803832 1.499375261 + -2.448979592t + t2 = 0.070803832 Factor a perfect square on the left side: (t + -1.224489796)(t + -1.224489796) = 0.070803832 Calculate the square root of the right side: 0.266089895 Break this problem into two subproblems by setting (t + -1.224489796) equal to 0.266089895 and -0.266089895.Subproblem 1
t + -1.224489796 = 0.266089895 Simplifying t + -1.224489796 = 0.266089895 Reorder the terms: -1.224489796 + t = 0.266089895 Solving -1.224489796 + t = 0.266089895 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.224489796' to each side of the equation. -1.224489796 + 1.224489796 + t = 0.266089895 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + t = 0.266089895 + 1.224489796 t = 0.266089895 + 1.224489796 Combine like terms: 0.266089895 + 1.224489796 = 1.490579691 t = 1.490579691 Simplifying t = 1.490579691Subproblem 2
t + -1.224489796 = -0.266089895 Simplifying t + -1.224489796 = -0.266089895 Reorder the terms: -1.224489796 + t = -0.266089895 Solving -1.224489796 + t = -0.266089895 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.224489796' to each side of the equation. -1.224489796 + 1.224489796 + t = -0.266089895 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + t = -0.266089895 + 1.224489796 t = -0.266089895 + 1.224489796 Combine like terms: -0.266089895 + 1.224489796 = 0.958399901 t = 0.958399901 Simplifying t = 0.958399901Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.490579691, 0.958399901}
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