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Simplifying -5t2 + 11t + 54 = 0 Reorder the terms: 54 + 11t + -5t2 = 0 Solving 54 + 11t + -5t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -10.8 + -2.2t + t2 = 0 Move the constant term to the right: Add '10.8' to each side of the equation. -10.8 + -2.2t + 10.8 + t2 = 0 + 10.8 Reorder the terms: -10.8 + 10.8 + -2.2t + t2 = 0 + 10.8 Combine like terms: -10.8 + 10.8 = 0.0 0.0 + -2.2t + t2 = 0 + 10.8 -2.2t + t2 = 0 + 10.8 Combine like terms: 0 + 10.8 = 10.8 -2.2t + t2 = 10.8 The t term is -2.2t. Take half its coefficient (-1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. -2.2t + 1.21 + t2 = 10.8 + 1.21 Reorder the terms: 1.21 + -2.2t + t2 = 10.8 + 1.21 Combine like terms: 10.8 + 1.21 = 12.01 1.21 + -2.2t + t2 = 12.01 Factor a perfect square on the left side: (t + -1.1)(t + -1.1) = 12.01 Calculate the square root of the right side: 3.46554469 Break this problem into two subproblems by setting (t + -1.1) equal to 3.46554469 and -3.46554469.Subproblem 1
t + -1.1 = 3.46554469 Simplifying t + -1.1 = 3.46554469 Reorder the terms: -1.1 + t = 3.46554469 Solving -1.1 + t = 3.46554469 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + t = 3.46554469 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + t = 3.46554469 + 1.1 t = 3.46554469 + 1.1 Combine like terms: 3.46554469 + 1.1 = 4.56554469 t = 4.56554469 Simplifying t = 4.56554469Subproblem 2
t + -1.1 = -3.46554469 Simplifying t + -1.1 = -3.46554469 Reorder the terms: -1.1 + t = -3.46554469 Solving -1.1 + t = -3.46554469 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + t = -3.46554469 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + t = -3.46554469 + 1.1 t = -3.46554469 + 1.1 Combine like terms: -3.46554469 + 1.1 = -2.36554469 t = -2.36554469 Simplifying t = -2.36554469Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.56554469, -2.36554469}
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