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Simplifying 44t2 + t = 96 Reorder the terms: t + 44t2 = 96 Solving t + 44t2 = 96 Solving for variable 't'. Reorder the terms: -96 + t + 44t2 = 96 + -96 Combine like terms: 96 + -96 = 0 -96 + t + 44t2 = 0 Begin completing the square. Divide all terms by 44 the coefficient of the squared term: Divide each side by '44'. -2.181818182 + 0.02272727273t + t2 = 0 Move the constant term to the right: Add '2.181818182' to each side of the equation. -2.181818182 + 0.02272727273t + 2.181818182 + t2 = 0 + 2.181818182 Reorder the terms: -2.181818182 + 2.181818182 + 0.02272727273t + t2 = 0 + 2.181818182 Combine like terms: -2.181818182 + 2.181818182 = 0.000000000 0.000000000 + 0.02272727273t + t2 = 0 + 2.181818182 0.02272727273t + t2 = 0 + 2.181818182 Combine like terms: 0 + 2.181818182 = 2.181818182 0.02272727273t + t2 = 2.181818182 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.02272727273t + 0.25 + t2 = 2.181818182 + 0.25 Reorder the terms: 0.25 + 0.02272727273t + t2 = 2.181818182 + 0.25 Combine like terms: 2.181818182 + 0.25 = 2.431818182 0.25 + 0.02272727273t + t2 = 2.431818182 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 2.431818182 Calculate the square root of the right side: 1.5594288 Break this problem into two subproblems by setting (t + 0.5) equal to 1.5594288 and -1.5594288.Subproblem 1
t + 0.5 = 1.5594288 Simplifying t + 0.5 = 1.5594288 Reorder the terms: 0.5 + t = 1.5594288 Solving 0.5 + t = 1.5594288 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = 1.5594288 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 1.5594288 + -0.5 t = 1.5594288 + -0.5 Combine like terms: 1.5594288 + -0.5 = 1.0594288 t = 1.0594288 Simplifying t = 1.0594288Subproblem 2
t + 0.5 = -1.5594288 Simplifying t + 0.5 = -1.5594288 Reorder the terms: 0.5 + t = -1.5594288 Solving 0.5 + t = -1.5594288 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = -1.5594288 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -1.5594288 + -0.5 t = -1.5594288 + -0.5 Combine like terms: -1.5594288 + -0.5 = -2.0594288 t = -2.0594288 Simplifying t = -2.0594288Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.0594288, -2.0594288}
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