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Simplifying 10t2 + 9t + -28 = 0 Reorder the terms: -28 + 9t + 10t2 = 0 Solving -28 + 9t + 10t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -2.8 + 0.9t + t2 = 0 Move the constant term to the right: Add '2.8' to each side of the equation. -2.8 + 0.9t + 2.8 + t2 = 0 + 2.8 Reorder the terms: -2.8 + 2.8 + 0.9t + t2 = 0 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + 0.9t + t2 = 0 + 2.8 0.9t + t2 = 0 + 2.8 Combine like terms: 0 + 2.8 = 2.8 0.9t + t2 = 2.8 The t term is 0.9t. Take half its coefficient (0.45). Square it (0.2025) and add it to both sides. Add '0.2025' to each side of the equation. 0.9t + 0.2025 + t2 = 2.8 + 0.2025 Reorder the terms: 0.2025 + 0.9t + t2 = 2.8 + 0.2025 Combine like terms: 2.8 + 0.2025 = 3.0025 0.2025 + 0.9t + t2 = 3.0025 Factor a perfect square on the left side: (t + 0.45)(t + 0.45) = 3.0025 Calculate the square root of the right side: 1.732772345 Break this problem into two subproblems by setting (t + 0.45) equal to 1.732772345 and -1.732772345.Subproblem 1
t + 0.45 = 1.732772345 Simplifying t + 0.45 = 1.732772345 Reorder the terms: 0.45 + t = 1.732772345 Solving 0.45 + t = 1.732772345 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.45' to each side of the equation. 0.45 + -0.45 + t = 1.732772345 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + t = 1.732772345 + -0.45 t = 1.732772345 + -0.45 Combine like terms: 1.732772345 + -0.45 = 1.282772345 t = 1.282772345 Simplifying t = 1.282772345Subproblem 2
t + 0.45 = -1.732772345 Simplifying t + 0.45 = -1.732772345 Reorder the terms: 0.45 + t = -1.732772345 Solving 0.45 + t = -1.732772345 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.45' to each side of the equation. 0.45 + -0.45 + t = -1.732772345 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + t = -1.732772345 + -0.45 t = -1.732772345 + -0.45 Combine like terms: -1.732772345 + -0.45 = -2.182772345 t = -2.182772345 Simplifying t = -2.182772345Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.282772345, -2.182772345}
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