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Simplifying 25 = 12t + 4.9t2 Solving 25 = 12t + 4.9t2 Solving for variable 't'. Reorder the terms: 25 + -12t + -4.9t2 = 12t + -12t + 4.9t2 + -4.9t2 Combine like terms: 12t + -12t = 0 25 + -12t + -4.9t2 = 0 + 4.9t2 + -4.9t2 25 + -12t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 25 + -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'. -5.102040816 + 2.448979592t + t2 = 0 Move the constant term to the right: Add '5.102040816' to each side of the equation. -5.102040816 + 2.448979592t + 5.102040816 + t2 = 0 + 5.102040816 Reorder the terms: -5.102040816 + 5.102040816 + 2.448979592t + t2 = 0 + 5.102040816 Combine like terms: -5.102040816 + 5.102040816 = 0.000000000 0.000000000 + 2.448979592t + t2 = 0 + 5.102040816 2.448979592t + t2 = 0 + 5.102040816 Combine like terms: 0 + 5.102040816 = 5.102040816 2.448979592t + t2 = 5.102040816 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 = 5.102040816 + 1.499375261 Reorder the terms: 1.499375261 + 2.448979592t + t2 = 5.102040816 + 1.499375261 Combine like terms: 5.102040816 + 1.499375261 = 6.601416077 1.499375261 + 2.448979592t + t2 = 6.601416077 Factor a perfect square on the left side: (t + 1.224489796)(t + 1.224489796) = 6.601416077 Calculate the square root of the right side: 2.569322105 Break this problem into two subproblems by setting (t + 1.224489796) equal to 2.569322105 and -2.569322105.Subproblem 1
t + 1.224489796 = 2.569322105 Simplifying t + 1.224489796 = 2.569322105 Reorder the terms: 1.224489796 + t = 2.569322105 Solving 1.224489796 + t = 2.569322105 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 = 2.569322105 + -1.224489796 Combine like terms: 1.224489796 + -1.224489796 = 0.000000000 0.000000000 + t = 2.569322105 + -1.224489796 t = 2.569322105 + -1.224489796 Combine like terms: 2.569322105 + -1.224489796 = 1.344832309 t = 1.344832309 Simplifying t = 1.344832309Subproblem 2
t + 1.224489796 = -2.569322105 Simplifying t + 1.224489796 = -2.569322105 Reorder the terms: 1.224489796 + t = -2.569322105 Solving 1.224489796 + t = -2.569322105 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 = -2.569322105 + -1.224489796 Combine like terms: 1.224489796 + -1.224489796 = 0.000000000 0.000000000 + t = -2.569322105 + -1.224489796 t = -2.569322105 + -1.224489796 Combine like terms: -2.569322105 + -1.224489796 = -3.793811901 t = -3.793811901 Simplifying t = -3.793811901Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.344832309, -3.793811901}
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