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Simplifying 4t2 + -9t + -37 = 0 Reorder the terms: -37 + -9t + 4t2 = 0 Solving -37 + -9t + 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'. -9.25 + -2.25t + t2 = 0 Move the constant term to the right: Add '9.25' to each side of the equation. -9.25 + -2.25t + 9.25 + t2 = 0 + 9.25 Reorder the terms: -9.25 + 9.25 + -2.25t + t2 = 0 + 9.25 Combine like terms: -9.25 + 9.25 = 0.00 0.00 + -2.25t + t2 = 0 + 9.25 -2.25t + t2 = 0 + 9.25 Combine like terms: 0 + 9.25 = 9.25 -2.25t + t2 = 9.25 The t term is -2.25t. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25t + 1.265625 + t2 = 9.25 + 1.265625 Reorder the terms: 1.265625 + -2.25t + t2 = 9.25 + 1.265625 Combine like terms: 9.25 + 1.265625 = 10.515625 1.265625 + -2.25t + t2 = 10.515625 Factor a perfect square on the left side: (t + -1.125)(t + -1.125) = 10.515625 Calculate the square root of the right side: 3.242780443 Break this problem into two subproblems by setting (t + -1.125) equal to 3.242780443 and -3.242780443.Subproblem 1
t + -1.125 = 3.242780443 Simplifying t + -1.125 = 3.242780443 Reorder the terms: -1.125 + t = 3.242780443 Solving -1.125 + t = 3.242780443 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + t = 3.242780443 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + t = 3.242780443 + 1.125 t = 3.242780443 + 1.125 Combine like terms: 3.242780443 + 1.125 = 4.367780443 t = 4.367780443 Simplifying t = 4.367780443Subproblem 2
t + -1.125 = -3.242780443 Simplifying t + -1.125 = -3.242780443 Reorder the terms: -1.125 + t = -3.242780443 Solving -1.125 + t = -3.242780443 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + t = -3.242780443 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + t = -3.242780443 + 1.125 t = -3.242780443 + 1.125 Combine like terms: -3.242780443 + 1.125 = -2.117780443 t = -2.117780443 Simplifying t = -2.117780443Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.367780443, -2.117780443}
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