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Simplifying -16t2 + 21t + 4 = 0 Reorder the terms: 4 + 21t + -16t2 = 0 Solving 4 + 21t + -16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.25 + -1.3125t + t2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -1.3125t + 0.25 + t2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -1.3125t + t2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -1.3125t + t2 = 0 + 0.25 -1.3125t + t2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -1.3125t + t2 = 0.25 The t term is -1.3125t. Take half its coefficient (-0.65625). Square it (0.4306640625) and add it to both sides. Add '0.4306640625' to each side of the equation. -1.3125t + 0.4306640625 + t2 = 0.25 + 0.4306640625 Reorder the terms: 0.4306640625 + -1.3125t + t2 = 0.25 + 0.4306640625 Combine like terms: 0.25 + 0.4306640625 = 0.6806640625 0.4306640625 + -1.3125t + t2 = 0.6806640625 Factor a perfect square on the left side: (t + -0.65625)(t + -0.65625) = 0.6806640625 Calculate the square root of the right side: 0.825023674 Break this problem into two subproblems by setting (t + -0.65625) equal to 0.825023674 and -0.825023674.Subproblem 1
t + -0.65625 = 0.825023674 Simplifying t + -0.65625 = 0.825023674 Reorder the terms: -0.65625 + t = 0.825023674 Solving -0.65625 + t = 0.825023674 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.65625' to each side of the equation. -0.65625 + 0.65625 + t = 0.825023674 + 0.65625 Combine like terms: -0.65625 + 0.65625 = 0.00000 0.00000 + t = 0.825023674 + 0.65625 t = 0.825023674 + 0.65625 Combine like terms: 0.825023674 + 0.65625 = 1.481273674 t = 1.481273674 Simplifying t = 1.481273674Subproblem 2
t + -0.65625 = -0.825023674 Simplifying t + -0.65625 = -0.825023674 Reorder the terms: -0.65625 + t = -0.825023674 Solving -0.65625 + t = -0.825023674 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.65625' to each side of the equation. -0.65625 + 0.65625 + t = -0.825023674 + 0.65625 Combine like terms: -0.65625 + 0.65625 = 0.00000 0.00000 + t = -0.825023674 + 0.65625 t = -0.825023674 + 0.65625 Combine like terms: -0.825023674 + 0.65625 = -0.168773674 t = -0.168773674 Simplifying t = -0.168773674Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.481273674, -0.168773674}
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