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Simplifying t2 + -30t + 112.5 = 0 Reorder the terms: 112.5 + -30t + t2 = 0 Solving 112.5 + -30t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-112.5' to each side of the equation. 112.5 + -30t + -112.5 + t2 = 0 + -112.5 Reorder the terms: 112.5 + -112.5 + -30t + t2 = 0 + -112.5 Combine like terms: 112.5 + -112.5 = 0.0 0.0 + -30t + t2 = 0 + -112.5 -30t + t2 = 0 + -112.5 Combine like terms: 0 + -112.5 = -112.5 -30t + t2 = -112.5 The t term is -30t. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30t + 225 + t2 = -112.5 + 225 Reorder the terms: 225 + -30t + t2 = -112.5 + 225 Combine like terms: -112.5 + 225 = 112.5 225 + -30t + t2 = 112.5 Factor a perfect square on the left side: (t + -15)(t + -15) = 112.5 Calculate the square root of the right side: 10.606601718 Break this problem into two subproblems by setting (t + -15) equal to 10.606601718 and -10.606601718.Subproblem 1
t + -15 = 10.606601718 Simplifying t + -15 = 10.606601718 Reorder the terms: -15 + t = 10.606601718 Solving -15 + t = 10.606601718 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + t = 10.606601718 + 15 Combine like terms: -15 + 15 = 0 0 + t = 10.606601718 + 15 t = 10.606601718 + 15 Combine like terms: 10.606601718 + 15 = 25.606601718 t = 25.606601718 Simplifying t = 25.606601718Subproblem 2
t + -15 = -10.606601718 Simplifying t + -15 = -10.606601718 Reorder the terms: -15 + t = -10.606601718 Solving -15 + t = -10.606601718 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + t = -10.606601718 + 15 Combine like terms: -15 + 15 = 0 0 + t = -10.606601718 + 15 t = -10.606601718 + 15 Combine like terms: -10.606601718 + 15 = 4.393398282 t = 4.393398282 Simplifying t = 4.393398282Solution
The solution to the problem is based on the solutions from the subproblems. t = {25.606601718, 4.393398282}
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