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Simplifying -16t2 + -19t + 200 = 0 Reorder the terms: 200 + -19t + -16t2 = 0 Solving 200 + -19t + -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'. -12.5 + 1.1875t + t2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + 1.1875t + 12.5 + t2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + 1.1875t + t2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + 1.1875t + t2 = 0 + 12.5 1.1875t + t2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 1.1875t + t2 = 12.5 The t term is 1.1875t. Take half its coefficient (0.59375). Square it (0.3525390625) and add it to both sides. Add '0.3525390625' to each side of the equation. 1.1875t + 0.3525390625 + t2 = 12.5 + 0.3525390625 Reorder the terms: 0.3525390625 + 1.1875t + t2 = 12.5 + 0.3525390625 Combine like terms: 12.5 + 0.3525390625 = 12.8525390625 0.3525390625 + 1.1875t + t2 = 12.8525390625 Factor a perfect square on the left side: (t + 0.59375)(t + 0.59375) = 12.8525390625 Calculate the square root of the right side: 3.585043802 Break this problem into two subproblems by setting (t + 0.59375) equal to 3.585043802 and -3.585043802.Subproblem 1
t + 0.59375 = 3.585043802 Simplifying t + 0.59375 = 3.585043802 Reorder the terms: 0.59375 + t = 3.585043802 Solving 0.59375 + t = 3.585043802 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.59375' to each side of the equation. 0.59375 + -0.59375 + t = 3.585043802 + -0.59375 Combine like terms: 0.59375 + -0.59375 = 0.00000 0.00000 + t = 3.585043802 + -0.59375 t = 3.585043802 + -0.59375 Combine like terms: 3.585043802 + -0.59375 = 2.991293802 t = 2.991293802 Simplifying t = 2.991293802Subproblem 2
t + 0.59375 = -3.585043802 Simplifying t + 0.59375 = -3.585043802 Reorder the terms: 0.59375 + t = -3.585043802 Solving 0.59375 + t = -3.585043802 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.59375' to each side of the equation. 0.59375 + -0.59375 + t = -3.585043802 + -0.59375 Combine like terms: 0.59375 + -0.59375 = 0.00000 0.00000 + t = -3.585043802 + -0.59375 t = -3.585043802 + -0.59375 Combine like terms: -3.585043802 + -0.59375 = -4.178793802 t = -4.178793802 Simplifying t = -4.178793802Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.991293802, -4.178793802}
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