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Simplifying 5t2 + -13t + -96 = 0 Reorder the terms: -96 + -13t + 5t2 = 0 Solving -96 + -13t + 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'. -19.2 + -2.6t + t2 = 0 Move the constant term to the right: Add '19.2' to each side of the equation. -19.2 + -2.6t + 19.2 + t2 = 0 + 19.2 Reorder the terms: -19.2 + 19.2 + -2.6t + t2 = 0 + 19.2 Combine like terms: -19.2 + 19.2 = 0.0 0.0 + -2.6t + t2 = 0 + 19.2 -2.6t + t2 = 0 + 19.2 Combine like terms: 0 + 19.2 = 19.2 -2.6t + t2 = 19.2 The t term is -2.6t. Take half its coefficient (-1.3). Square it (1.69) and add it to both sides. Add '1.69' to each side of the equation. -2.6t + 1.69 + t2 = 19.2 + 1.69 Reorder the terms: 1.69 + -2.6t + t2 = 19.2 + 1.69 Combine like terms: 19.2 + 1.69 = 20.89 1.69 + -2.6t + t2 = 20.89 Factor a perfect square on the left side: (t + -1.3)(t + -1.3) = 20.89 Calculate the square root of the right side: 4.570557953 Break this problem into two subproblems by setting (t + -1.3) equal to 4.570557953 and -4.570557953.Subproblem 1
t + -1.3 = 4.570557953 Simplifying t + -1.3 = 4.570557953 Reorder the terms: -1.3 + t = 4.570557953 Solving -1.3 + t = 4.570557953 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + t = 4.570557953 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + t = 4.570557953 + 1.3 t = 4.570557953 + 1.3 Combine like terms: 4.570557953 + 1.3 = 5.870557953 t = 5.870557953 Simplifying t = 5.870557953Subproblem 2
t + -1.3 = -4.570557953 Simplifying t + -1.3 = -4.570557953 Reorder the terms: -1.3 + t = -4.570557953 Solving -1.3 + t = -4.570557953 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + t = -4.570557953 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + t = -4.570557953 + 1.3 t = -4.570557953 + 1.3 Combine like terms: -4.570557953 + 1.3 = -3.270557953 t = -3.270557953 Simplifying t = -3.270557953Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.870557953, -3.270557953}
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