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Simplifying 6 = -16t2 + 25t Reorder the terms: 6 = 25t + -16t2 Solving 6 = 25t + -16t2 Solving for variable 't'. Reorder the terms: 6 + -25t + 16t2 = 25t + -25t + -16t2 + 16t2 Combine like terms: 25t + -25t = 0 6 + -25t + 16t2 = 0 + -16t2 + 16t2 6 + -25t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 6 + -25t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.375 + -1.5625t + t2 = 0 Move the constant term to the right: Add '-0.375' to each side of the equation. 0.375 + -1.5625t + -0.375 + t2 = 0 + -0.375 Reorder the terms: 0.375 + -0.375 + -1.5625t + t2 = 0 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + -1.5625t + t2 = 0 + -0.375 -1.5625t + t2 = 0 + -0.375 Combine like terms: 0 + -0.375 = -0.375 -1.5625t + t2 = -0.375 The t term is -1.5625t. Take half its coefficient (-0.78125). Square it (0.6103515625) and add it to both sides. Add '0.6103515625' to each side of the equation. -1.5625t + 0.6103515625 + t2 = -0.375 + 0.6103515625 Reorder the terms: 0.6103515625 + -1.5625t + t2 = -0.375 + 0.6103515625 Combine like terms: -0.375 + 0.6103515625 = 0.2353515625 0.6103515625 + -1.5625t + t2 = 0.2353515625 Factor a perfect square on the left side: (t + -0.78125)(t + -0.78125) = 0.2353515625 Calculate the square root of the right side: 0.485130459 Break this problem into two subproblems by setting (t + -0.78125) equal to 0.485130459 and -0.485130459.Subproblem 1
t + -0.78125 = 0.485130459 Simplifying t + -0.78125 = 0.485130459 Reorder the terms: -0.78125 + t = 0.485130459 Solving -0.78125 + t = 0.485130459 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.78125' to each side of the equation. -0.78125 + 0.78125 + t = 0.485130459 + 0.78125 Combine like terms: -0.78125 + 0.78125 = 0.00000 0.00000 + t = 0.485130459 + 0.78125 t = 0.485130459 + 0.78125 Combine like terms: 0.485130459 + 0.78125 = 1.266380459 t = 1.266380459 Simplifying t = 1.266380459Subproblem 2
t + -0.78125 = -0.485130459 Simplifying t + -0.78125 = -0.485130459 Reorder the terms: -0.78125 + t = -0.485130459 Solving -0.78125 + t = -0.485130459 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.78125' to each side of the equation. -0.78125 + 0.78125 + t = -0.485130459 + 0.78125 Combine like terms: -0.78125 + 0.78125 = 0.00000 0.00000 + t = -0.485130459 + 0.78125 t = -0.485130459 + 0.78125 Combine like terms: -0.485130459 + 0.78125 = 0.296119541 t = 0.296119541 Simplifying t = 0.296119541Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.266380459, 0.296119541}
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