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Simplifying 700 = -4.9t2 + 120t + 3 Reorder the terms: 700 = 3 + 120t + -4.9t2 Solving 700 = 3 + 120t + -4.9t2 Solving for variable 't'. Combine like terms: 700 + -3 = 697 697 + -120t + 4.9t2 = 3 + 120t + -4.9t2 + -3 + -120t + 4.9t2 Reorder the terms: 697 + -120t + 4.9t2 = 3 + -3 + 120t + -120t + -4.9t2 + 4.9t2 Combine like terms: 3 + -3 = 0 697 + -120t + 4.9t2 = 0 + 120t + -120t + -4.9t2 + 4.9t2 697 + -120t + 4.9t2 = 120t + -120t + -4.9t2 + 4.9t2 Combine like terms: 120t + -120t = 0 697 + -120t + 4.9t2 = 0 + -4.9t2 + 4.9t2 697 + -120t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 697 + -120t + 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'. 142.244898 + -24.48979592t + t2 = 0 Move the constant term to the right: Add '-142.244898' to each side of the equation. 142.244898 + -24.48979592t + -142.244898 + t2 = 0 + -142.244898 Reorder the terms: 142.244898 + -142.244898 + -24.48979592t + t2 = 0 + -142.244898 Combine like terms: 142.244898 + -142.244898 = 0.000000 0.000000 + -24.48979592t + t2 = 0 + -142.244898 -24.48979592t + t2 = 0 + -142.244898 Combine like terms: 0 + -142.244898 = -142.244898 -24.48979592t + t2 = -142.244898 The t term is -24.48979592t. Take half its coefficient (-12.24489796). Square it (149.9375261) and add it to both sides. Add '149.9375261' to each side of the equation. -24.48979592t + 149.9375261 + t2 = -142.244898 + 149.9375261 Reorder the terms: 149.9375261 + -24.48979592t + t2 = -142.244898 + 149.9375261 Combine like terms: -142.244898 + 149.9375261 = 7.6926281 149.9375261 + -24.48979592t + t2 = 7.6926281 Factor a perfect square on the left side: (t + -12.24489796)(t + -12.24489796) = 7.6926281 Calculate the square root of the right side: 2.773558743 Break this problem into two subproblems by setting (t + -12.24489796) equal to 2.773558743 and -2.773558743.Subproblem 1
t + -12.24489796 = 2.773558743 Simplifying t + -12.24489796 = 2.773558743 Reorder the terms: -12.24489796 + t = 2.773558743 Solving -12.24489796 + t = 2.773558743 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12.24489796' to each side of the equation. -12.24489796 + 12.24489796 + t = 2.773558743 + 12.24489796 Combine like terms: -12.24489796 + 12.24489796 = 0.00000000 0.00000000 + t = 2.773558743 + 12.24489796 t = 2.773558743 + 12.24489796 Combine like terms: 2.773558743 + 12.24489796 = 15.018456703 t = 15.018456703 Simplifying t = 15.018456703Subproblem 2
t + -12.24489796 = -2.773558743 Simplifying t + -12.24489796 = -2.773558743 Reorder the terms: -12.24489796 + t = -2.773558743 Solving -12.24489796 + t = -2.773558743 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12.24489796' to each side of the equation. -12.24489796 + 12.24489796 + t = -2.773558743 + 12.24489796 Combine like terms: -12.24489796 + 12.24489796 = 0.00000000 0.00000000 + t = -2.773558743 + 12.24489796 t = -2.773558743 + 12.24489796 Combine like terms: -2.773558743 + 12.24489796 = 9.471339217 t = 9.471339217 Simplifying t = 9.471339217Solution
The solution to the problem is based on the solutions from the subproblems. t = {15.018456703, 9.471339217}
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