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Simplifying 0 = -4.9t2 + 12.7t + 6 Reorder the terms: 0 = 6 + 12.7t + -4.9t2 Solving 0 = 6 + 12.7t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -6 = -6 -6 + -12.7t + 4.9t2 = 6 + 12.7t + -4.9t2 + -6 + -12.7t + 4.9t2 Reorder the terms: -6 + -12.7t + 4.9t2 = 6 + -6 + 12.7t + -12.7t + -4.9t2 + 4.9t2 Combine like terms: 6 + -6 = 0 -6 + -12.7t + 4.9t2 = 0 + 12.7t + -12.7t + -4.9t2 + 4.9t2 -6 + -12.7t + 4.9t2 = 12.7t + -12.7t + -4.9t2 + 4.9t2 Combine like terms: 12.7t + -12.7t = 0.0 -6 + -12.7t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2 -6 + -12.7t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -6 + -12.7t + 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'. -1.224489796 + -2.591836735t + t2 = 0 Move the constant term to the right: Add '1.224489796' to each side of the equation. -1.224489796 + -2.591836735t + 1.224489796 + t2 = 0 + 1.224489796 Reorder the terms: -1.224489796 + 1.224489796 + -2.591836735t + t2 = 0 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + -2.591836735t + t2 = 0 + 1.224489796 -2.591836735t + t2 = 0 + 1.224489796 Combine like terms: 0 + 1.224489796 = 1.224489796 -2.591836735t + t2 = 1.224489796 The t term is -2.591836735t. Take half its coefficient (-1.295918368). Square it (1.679404417) and add it to both sides. Add '1.679404417' to each side of the equation. -2.591836735t + 1.679404417 + t2 = 1.224489796 + 1.679404417 Reorder the terms: 1.679404417 + -2.591836735t + t2 = 1.224489796 + 1.679404417 Combine like terms: 1.224489796 + 1.679404417 = 2.903894213 1.679404417 + -2.591836735t + t2 = 2.903894213 Factor a perfect square on the left side: (t + -1.295918368)(t + -1.295918368) = 2.903894213 Calculate the square root of the right side: 1.704081633 Break this problem into two subproblems by setting (t + -1.295918368) equal to 1.704081633 and -1.704081633.Subproblem 1
t + -1.295918368 = 1.704081633 Simplifying t + -1.295918368 = 1.704081633 Reorder the terms: -1.295918368 + t = 1.704081633 Solving -1.295918368 + t = 1.704081633 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.295918368' to each side of the equation. -1.295918368 + 1.295918368 + t = 1.704081633 + 1.295918368 Combine like terms: -1.295918368 + 1.295918368 = 0.000000000 0.000000000 + t = 1.704081633 + 1.295918368 t = 1.704081633 + 1.295918368 Combine like terms: 1.704081633 + 1.295918368 = 3.000000001 t = 3.000000001 Simplifying t = 3.000000001Subproblem 2
t + -1.295918368 = -1.704081633 Simplifying t + -1.295918368 = -1.704081633 Reorder the terms: -1.295918368 + t = -1.704081633 Solving -1.295918368 + t = -1.704081633 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.295918368' to each side of the equation. -1.295918368 + 1.295918368 + t = -1.704081633 + 1.295918368 Combine like terms: -1.295918368 + 1.295918368 = 0.000000000 0.000000000 + t = -1.704081633 + 1.295918368 t = -1.704081633 + 1.295918368 Combine like terms: -1.704081633 + 1.295918368 = -0.408163265 t = -0.408163265 Simplifying t = -0.408163265Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.000000001, -0.408163265}
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