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Simplifying 4 = -16t2 + 19t + 5 Reorder the terms: 4 = 5 + 19t + -16t2 Solving 4 = 5 + 19t + -16t2 Solving for variable 't'. Combine like terms: 4 + -5 = -1 -1 + -19t + 16t2 = 5 + 19t + -16t2 + -5 + -19t + 16t2 Reorder the terms: -1 + -19t + 16t2 = 5 + -5 + 19t + -19t + -16t2 + 16t2 Combine like terms: 5 + -5 = 0 -1 + -19t + 16t2 = 0 + 19t + -19t + -16t2 + 16t2 -1 + -19t + 16t2 = 19t + -19t + -16t2 + 16t2 Combine like terms: 19t + -19t = 0 -1 + -19t + 16t2 = 0 + -16t2 + 16t2 -1 + -19t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -1 + -19t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.0625 + -1.1875t + t2 = 0 Move the constant term to the right: Add '0.0625' to each side of the equation. -0.0625 + -1.1875t + 0.0625 + t2 = 0 + 0.0625 Reorder the terms: -0.0625 + 0.0625 + -1.1875t + t2 = 0 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + -1.1875t + t2 = 0 + 0.0625 -1.1875t + t2 = 0 + 0.0625 Combine like terms: 0 + 0.0625 = 0.0625 -1.1875t + t2 = 0.0625 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 = 0.0625 + 0.3525390625 Reorder the terms: 0.3525390625 + -1.1875t + t2 = 0.0625 + 0.3525390625 Combine like terms: 0.0625 + 0.3525390625 = 0.4150390625 0.3525390625 + -1.1875t + t2 = 0.4150390625 Factor a perfect square on the left side: (t + -0.59375)(t + -0.59375) = 0.4150390625 Calculate the square root of the right side: 0.644235254 Break this problem into two subproblems by setting (t + -0.59375) equal to 0.644235254 and -0.644235254.Subproblem 1
t + -0.59375 = 0.644235254 Simplifying t + -0.59375 = 0.644235254 Reorder the terms: -0.59375 + t = 0.644235254 Solving -0.59375 + t = 0.644235254 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 = 0.644235254 + 0.59375 Combine like terms: -0.59375 + 0.59375 = 0.00000 0.00000 + t = 0.644235254 + 0.59375 t = 0.644235254 + 0.59375 Combine like terms: 0.644235254 + 0.59375 = 1.237985254 t = 1.237985254 Simplifying t = 1.237985254Subproblem 2
t + -0.59375 = -0.644235254 Simplifying t + -0.59375 = -0.644235254 Reorder the terms: -0.59375 + t = -0.644235254 Solving -0.59375 + t = -0.644235254 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 = -0.644235254 + 0.59375 Combine like terms: -0.59375 + 0.59375 = 0.00000 0.00000 + t = -0.644235254 + 0.59375 t = -0.644235254 + 0.59375 Combine like terms: -0.644235254 + 0.59375 = -0.050485254 t = -0.050485254 Simplifying t = -0.050485254Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.237985254, -0.050485254}
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