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Simplifying 4t2 + 19t + -28 = 0 Reorder the terms: -28 + 19t + 4t2 = 0 Solving -28 + 19t + 4t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -7 + 4.75t + t2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + 4.75t + 7 + t2 = 0 + 7 Reorder the terms: -7 + 7 + 4.75t + t2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 4.75t + t2 = 0 + 7 4.75t + t2 = 0 + 7 Combine like terms: 0 + 7 = 7 4.75t + t2 = 7 The t term is 4.75t. Take half its coefficient (2.375). Square it (5.640625) and add it to both sides. Add '5.640625' to each side of the equation. 4.75t + 5.640625 + t2 = 7 + 5.640625 Reorder the terms: 5.640625 + 4.75t + t2 = 7 + 5.640625 Combine like terms: 7 + 5.640625 = 12.640625 5.640625 + 4.75t + t2 = 12.640625 Factor a perfect square on the left side: (t + 2.375)(t + 2.375) = 12.640625 Calculate the square root of the right side: 3.555365663 Break this problem into two subproblems by setting (t + 2.375) equal to 3.555365663 and -3.555365663.Subproblem 1
t + 2.375 = 3.555365663 Simplifying t + 2.375 = 3.555365663 Reorder the terms: 2.375 + t = 3.555365663 Solving 2.375 + t = 3.555365663 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + t = 3.555365663 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + t = 3.555365663 + -2.375 t = 3.555365663 + -2.375 Combine like terms: 3.555365663 + -2.375 = 1.180365663 t = 1.180365663 Simplifying t = 1.180365663Subproblem 2
t + 2.375 = -3.555365663 Simplifying t + 2.375 = -3.555365663 Reorder the terms: 2.375 + t = -3.555365663 Solving 2.375 + t = -3.555365663 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + t = -3.555365663 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + t = -3.555365663 + -2.375 t = -3.555365663 + -2.375 Combine like terms: -3.555365663 + -2.375 = -5.930365663 t = -5.930365663 Simplifying t = -5.930365663Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.180365663, -5.930365663}
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