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Simplifying 11 = -16t2 + 42t Reorder the terms: 11 = 42t + -16t2 Solving 11 = 42t + -16t2 Solving for variable 't'. Reorder the terms: 11 + -42t + 16t2 = 42t + -42t + -16t2 + 16t2 Combine like terms: 42t + -42t = 0 11 + -42t + 16t2 = 0 + -16t2 + 16t2 11 + -42t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 11 + -42t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.6875 + -2.625t + t2 = 0 Move the constant term to the right: Add '-0.6875' to each side of the equation. 0.6875 + -2.625t + -0.6875 + t2 = 0 + -0.6875 Reorder the terms: 0.6875 + -0.6875 + -2.625t + t2 = 0 + -0.6875 Combine like terms: 0.6875 + -0.6875 = 0.0000 0.0000 + -2.625t + t2 = 0 + -0.6875 -2.625t + t2 = 0 + -0.6875 Combine like terms: 0 + -0.6875 = -0.6875 -2.625t + t2 = -0.6875 The t term is -2.625t. Take half its coefficient (-1.3125). Square it (1.72265625) and add it to both sides. Add '1.72265625' to each side of the equation. -2.625t + 1.72265625 + t2 = -0.6875 + 1.72265625 Reorder the terms: 1.72265625 + -2.625t + t2 = -0.6875 + 1.72265625 Combine like terms: -0.6875 + 1.72265625 = 1.03515625 1.72265625 + -2.625t + t2 = 1.03515625 Factor a perfect square on the left side: (t + -1.3125)(t + -1.3125) = 1.03515625 Calculate the square root of the right side: 1.017426287 Break this problem into two subproblems by setting (t + -1.3125) equal to 1.017426287 and -1.017426287.Subproblem 1
t + -1.3125 = 1.017426287 Simplifying t + -1.3125 = 1.017426287 Reorder the terms: -1.3125 + t = 1.017426287 Solving -1.3125 + t = 1.017426287 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.3125' to each side of the equation. -1.3125 + 1.3125 + t = 1.017426287 + 1.3125 Combine like terms: -1.3125 + 1.3125 = 0.0000 0.0000 + t = 1.017426287 + 1.3125 t = 1.017426287 + 1.3125 Combine like terms: 1.017426287 + 1.3125 = 2.329926287 t = 2.329926287 Simplifying t = 2.329926287Subproblem 2
t + -1.3125 = -1.017426287 Simplifying t + -1.3125 = -1.017426287 Reorder the terms: -1.3125 + t = -1.017426287 Solving -1.3125 + t = -1.017426287 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.3125' to each side of the equation. -1.3125 + 1.3125 + t = -1.017426287 + 1.3125 Combine like terms: -1.3125 + 1.3125 = 0.0000 0.0000 + t = -1.017426287 + 1.3125 t = -1.017426287 + 1.3125 Combine like terms: -1.017426287 + 1.3125 = 0.295073713 t = 0.295073713 Simplifying t = 0.295073713Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.329926287, 0.295073713}
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