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Simplifying 0.25t2 + -4.556t + -7.7452 = 0 Reorder the terms: -7.7452 + -4.556t + 0.25t2 = 0 Solving -7.7452 + -4.556t + 0.25t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. -30.9808 + -18.224t + t2 = 0 Move the constant term to the right: Add '30.9808' to each side of the equation. -30.9808 + -18.224t + 30.9808 + t2 = 0 + 30.9808 Reorder the terms: -30.9808 + 30.9808 + -18.224t + t2 = 0 + 30.9808 Combine like terms: -30.9808 + 30.9808 = 0.0000 0.0000 + -18.224t + t2 = 0 + 30.9808 -18.224t + t2 = 0 + 30.9808 Combine like terms: 0 + 30.9808 = 30.9808 -18.224t + t2 = 30.9808 The t term is -18.224t. Take half its coefficient (-9.112). Square it (83.028544) and add it to both sides. Add '83.028544' to each side of the equation. -18.224t + 83.028544 + t2 = 30.9808 + 83.028544 Reorder the terms: 83.028544 + -18.224t + t2 = 30.9808 + 83.028544 Combine like terms: 30.9808 + 83.028544 = 114.009344 83.028544 + -18.224t + t2 = 114.009344 Factor a perfect square on the left side: (t + -9.112)(t + -9.112) = 114.009344 Calculate the square root of the right side: 10.677515816 Break this problem into two subproblems by setting (t + -9.112) equal to 10.677515816 and -10.677515816.Subproblem 1
t + -9.112 = 10.677515816 Simplifying t + -9.112 = 10.677515816 Reorder the terms: -9.112 + t = 10.677515816 Solving -9.112 + t = 10.677515816 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9.112' to each side of the equation. -9.112 + 9.112 + t = 10.677515816 + 9.112 Combine like terms: -9.112 + 9.112 = 0.000 0.000 + t = 10.677515816 + 9.112 t = 10.677515816 + 9.112 Combine like terms: 10.677515816 + 9.112 = 19.789515816 t = 19.789515816 Simplifying t = 19.789515816Subproblem 2
t + -9.112 = -10.677515816 Simplifying t + -9.112 = -10.677515816 Reorder the terms: -9.112 + t = -10.677515816 Solving -9.112 + t = -10.677515816 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9.112' to each side of the equation. -9.112 + 9.112 + t = -10.677515816 + 9.112 Combine like terms: -9.112 + 9.112 = 0.000 0.000 + t = -10.677515816 + 9.112 t = -10.677515816 + 9.112 Combine like terms: -10.677515816 + 9.112 = -1.565515816 t = -1.565515816 Simplifying t = -1.565515816Solution
The solution to the problem is based on the solutions from the subproblems. t = {19.789515816, -1.565515816}
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