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Simplifying 57 = -12t + 5t2 Solving 57 = -12t + 5t2 Solving for variable 't'. Reorder the terms: 57 + 12t + -5t2 = -12t + 12t + 5t2 + -5t2 Combine like terms: -12t + 12t = 0 57 + 12t + -5t2 = 0 + 5t2 + -5t2 57 + 12t + -5t2 = 5t2 + -5t2 Combine like terms: 5t2 + -5t2 = 0 57 + 12t + -5t2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -11.4 + -2.4t + t2 = 0 Move the constant term to the right: Add '11.4' to each side of the equation. -11.4 + -2.4t + 11.4 + t2 = 0 + 11.4 Reorder the terms: -11.4 + 11.4 + -2.4t + t2 = 0 + 11.4 Combine like terms: -11.4 + 11.4 = 0.0 0.0 + -2.4t + t2 = 0 + 11.4 -2.4t + t2 = 0 + 11.4 Combine like terms: 0 + 11.4 = 11.4 -2.4t + t2 = 11.4 The t term is -2.4t. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4t + 1.44 + t2 = 11.4 + 1.44 Reorder the terms: 1.44 + -2.4t + t2 = 11.4 + 1.44 Combine like terms: 11.4 + 1.44 = 12.84 1.44 + -2.4t + t2 = 12.84 Factor a perfect square on the left side: (t + -1.2)(t + -1.2) = 12.84 Calculate the square root of the right side: 3.583294573 Break this problem into two subproblems by setting (t + -1.2) equal to 3.583294573 and -3.583294573.Subproblem 1
t + -1.2 = 3.583294573 Simplifying t + -1.2 = 3.583294573 Reorder the terms: -1.2 + t = 3.583294573 Solving -1.2 + t = 3.583294573 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + t = 3.583294573 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + t = 3.583294573 + 1.2 t = 3.583294573 + 1.2 Combine like terms: 3.583294573 + 1.2 = 4.783294573 t = 4.783294573 Simplifying t = 4.783294573Subproblem 2
t + -1.2 = -3.583294573 Simplifying t + -1.2 = -3.583294573 Reorder the terms: -1.2 + t = -3.583294573 Solving -1.2 + t = -3.583294573 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + t = -3.583294573 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + t = -3.583294573 + 1.2 t = -3.583294573 + 1.2 Combine like terms: -3.583294573 + 1.2 = -2.383294573 t = -2.383294573 Simplifying t = -2.383294573Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.783294573, -2.383294573}
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