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Simplifying t(t + -2) = 22.5 Reorder the terms: t(-2 + t) = 22.5 (-2 * t + t * t) = 22.5 (-2t + t2) = 22.5 Solving -2t + t2 = 22.5 Solving for variable 't'. Reorder the terms: -22.5 + -2t + t2 = 22.5 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 -22.5 + -2t + t2 = 0.0 Begin completing the square. Move the constant term to the right: Add '22.5' to each side of the equation. -22.5 + -2t + 22.5 + t2 = 0.0 + 22.5 Reorder the terms: -22.5 + 22.5 + -2t + t2 = 0.0 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + -2t + t2 = 0.0 + 22.5 -2t + t2 = 0.0 + 22.5 Combine like terms: 0.0 + 22.5 = 22.5 -2t + t2 = 22.5 The t term is -2t. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2t + 1 + t2 = 22.5 + 1 Reorder the terms: 1 + -2t + t2 = 22.5 + 1 Combine like terms: 22.5 + 1 = 23.5 1 + -2t + t2 = 23.5 Factor a perfect square on the left side: (t + -1)(t + -1) = 23.5 Calculate the square root of the right side: 4.847679857 Break this problem into two subproblems by setting (t + -1) equal to 4.847679857 and -4.847679857.Subproblem 1
t + -1 = 4.847679857 Simplifying t + -1 = 4.847679857 Reorder the terms: -1 + t = 4.847679857 Solving -1 + t = 4.847679857 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + t = 4.847679857 + 1 Combine like terms: -1 + 1 = 0 0 + t = 4.847679857 + 1 t = 4.847679857 + 1 Combine like terms: 4.847679857 + 1 = 5.847679857 t = 5.847679857 Simplifying t = 5.847679857Subproblem 2
t + -1 = -4.847679857 Simplifying t + -1 = -4.847679857 Reorder the terms: -1 + t = -4.847679857 Solving -1 + t = -4.847679857 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + t = -4.847679857 + 1 Combine like terms: -1 + 1 = 0 0 + t = -4.847679857 + 1 t = -4.847679857 + 1 Combine like terms: -4.847679857 + 1 = -3.847679857 t = -3.847679857 Simplifying t = -3.847679857Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.847679857, -3.847679857}
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