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Simplifying -5t + -2 = -9t2 Reorder the terms: -2 + -5t = -9t2 Solving -2 + -5t = -9t2 Solving for variable 't'. Combine like terms: -9t2 + 9t2 = 0 -2 + -5t + 9t2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.2222222222 + -0.5555555556t + t2 = 0 Move the constant term to the right: Add '0.2222222222' to each side of the equation. -0.2222222222 + -0.5555555556t + 0.2222222222 + t2 = 0 + 0.2222222222 Reorder the terms: -0.2222222222 + 0.2222222222 + -0.5555555556t + t2 = 0 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + -0.5555555556t + t2 = 0 + 0.2222222222 -0.5555555556t + t2 = 0 + 0.2222222222 Combine like terms: 0 + 0.2222222222 = 0.2222222222 -0.5555555556t + t2 = 0.2222222222 The t term is -0.5555555556t. Take half its coefficient (-0.2777777778). Square it (0.07716049384) and add it to both sides. Add '0.07716049384' to each side of the equation. -0.5555555556t + 0.07716049384 + t2 = 0.2222222222 + 0.07716049384 Reorder the terms: 0.07716049384 + -0.5555555556t + t2 = 0.2222222222 + 0.07716049384 Combine like terms: 0.2222222222 + 0.07716049384 = 0.29938271604 0.07716049384 + -0.5555555556t + t2 = 0.29938271604 Factor a perfect square on the left side: (t + -0.2777777778)(t + -0.2777777778) = 0.29938271604 Calculate the square root of the right side: 0.547158767 Break this problem into two subproblems by setting (t + -0.2777777778) equal to 0.547158767 and -0.547158767.Subproblem 1
t + -0.2777777778 = 0.547158767 Simplifying t + -0.2777777778 = 0.547158767 Reorder the terms: -0.2777777778 + t = 0.547158767 Solving -0.2777777778 + t = 0.547158767 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.2777777778 + t = 0.547158767 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + t = 0.547158767 + 0.2777777778 t = 0.547158767 + 0.2777777778 Combine like terms: 0.547158767 + 0.2777777778 = 0.8249365448 t = 0.8249365448 Simplifying t = 0.8249365448Subproblem 2
t + -0.2777777778 = -0.547158767 Simplifying t + -0.2777777778 = -0.547158767 Reorder the terms: -0.2777777778 + t = -0.547158767 Solving -0.2777777778 + t = -0.547158767 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.2777777778 + t = -0.547158767 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + t = -0.547158767 + 0.2777777778 t = -0.547158767 + 0.2777777778 Combine like terms: -0.547158767 + 0.2777777778 = -0.2693809892 t = -0.2693809892 Simplifying t = -0.2693809892Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.8249365448, -0.2693809892}
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