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Simplifying t2 + -30t = 225 Reorder the terms: -30t + t2 = 225 Solving -30t + t2 = 225 Solving for variable 't'. Reorder the terms: -225 + -30t + t2 = 225 + -225 Combine like terms: 225 + -225 = 0 -225 + -30t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '225' to each side of the equation. -225 + -30t + 225 + t2 = 0 + 225 Reorder the terms: -225 + 225 + -30t + t2 = 0 + 225 Combine like terms: -225 + 225 = 0 0 + -30t + t2 = 0 + 225 -30t + t2 = 0 + 225 Combine like terms: 0 + 225 = 225 -30t + t2 = 225 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 = 225 + 225 Reorder the terms: 225 + -30t + t2 = 225 + 225 Combine like terms: 225 + 225 = 450 225 + -30t + t2 = 450 Factor a perfect square on the left side: (t + -15)(t + -15) = 450 Calculate the square root of the right side: 21.213203436 Break this problem into two subproblems by setting (t + -15) equal to 21.213203436 and -21.213203436.Subproblem 1
t + -15 = 21.213203436 Simplifying t + -15 = 21.213203436 Reorder the terms: -15 + t = 21.213203436 Solving -15 + t = 21.213203436 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 = 21.213203436 + 15 Combine like terms: -15 + 15 = 0 0 + t = 21.213203436 + 15 t = 21.213203436 + 15 Combine like terms: 21.213203436 + 15 = 36.213203436 t = 36.213203436 Simplifying t = 36.213203436Subproblem 2
t + -15 = -21.213203436 Simplifying t + -15 = -21.213203436 Reorder the terms: -15 + t = -21.213203436 Solving -15 + t = -21.213203436 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 = -21.213203436 + 15 Combine like terms: -15 + 15 = 0 0 + t = -21.213203436 + 15 t = -21.213203436 + 15 Combine like terms: -21.213203436 + 15 = -6.213203436 t = -6.213203436 Simplifying t = -6.213203436Solution
The solution to the problem is based on the solutions from the subproblems. t = {36.213203436, -6.213203436}
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