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Simplifying t2 + -3t + -40 = 10 Reorder the terms: -40 + -3t + t2 = 10 Solving -40 + -3t + t2 = 10 Solving for variable 't'. Reorder the terms: -40 + -10 + -3t + t2 = 10 + -10 Combine like terms: -40 + -10 = -50 -50 + -3t + t2 = 10 + -10 Combine like terms: 10 + -10 = 0 -50 + -3t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + -3t + 50 + t2 = 0 + 50 Reorder the terms: -50 + 50 + -3t + t2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -3t + t2 = 0 + 50 -3t + t2 = 0 + 50 Combine like terms: 0 + 50 = 50 -3t + t2 = 50 The t term is -3t. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3t + 2.25 + t2 = 50 + 2.25 Reorder the terms: 2.25 + -3t + t2 = 50 + 2.25 Combine like terms: 50 + 2.25 = 52.25 2.25 + -3t + t2 = 52.25 Factor a perfect square on the left side: (t + -1.5)(t + -1.5) = 52.25 Calculate the square root of the right side: 7.228416147 Break this problem into two subproblems by setting (t + -1.5) equal to 7.228416147 and -7.228416147.Subproblem 1
t + -1.5 = 7.228416147 Simplifying t + -1.5 = 7.228416147 Reorder the terms: -1.5 + t = 7.228416147 Solving -1.5 + t = 7.228416147 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + t = 7.228416147 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = 7.228416147 + 1.5 t = 7.228416147 + 1.5 Combine like terms: 7.228416147 + 1.5 = 8.728416147 t = 8.728416147 Simplifying t = 8.728416147Subproblem 2
t + -1.5 = -7.228416147 Simplifying t + -1.5 = -7.228416147 Reorder the terms: -1.5 + t = -7.228416147 Solving -1.5 + t = -7.228416147 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + t = -7.228416147 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = -7.228416147 + 1.5 t = -7.228416147 + 1.5 Combine like terms: -7.228416147 + 1.5 = -5.728416147 t = -5.728416147 Simplifying t = -5.728416147Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.728416147, -5.728416147}
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