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Simplifying t2 + -1.5t + -27 = 0 Reorder the terms: -27 + -1.5t + t2 = 0 Solving -27 + -1.5t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + -1.5t + 27 + t2 = 0 + 27 Reorder the terms: -27 + 27 + -1.5t + t2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -1.5t + t2 = 0 + 27 -1.5t + t2 = 0 + 27 Combine like terms: 0 + 27 = 27 -1.5t + t2 = 27 The t term is -1.5t. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5t + 0.5625 + t2 = 27 + 0.5625 Reorder the terms: 0.5625 + -1.5t + t2 = 27 + 0.5625 Combine like terms: 27 + 0.5625 = 27.5625 0.5625 + -1.5t + t2 = 27.5625 Factor a perfect square on the left side: (t + -0.75)(t + -0.75) = 27.5625 Calculate the square root of the right side: 5.25 Break this problem into two subproblems by setting (t + -0.75) equal to 5.25 and -5.25.Subproblem 1
t + -0.75 = 5.25 Simplifying t + -0.75 = 5.25 Reorder the terms: -0.75 + t = 5.25 Solving -0.75 + t = 5.25 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + t = 5.25 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + t = 5.25 + 0.75 t = 5.25 + 0.75 Combine like terms: 5.25 + 0.75 = 6 t = 6 Simplifying t = 6Subproblem 2
t + -0.75 = -5.25 Simplifying t + -0.75 = -5.25 Reorder the terms: -0.75 + t = -5.25 Solving -0.75 + t = -5.25 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + t = -5.25 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + t = -5.25 + 0.75 t = -5.25 + 0.75 Combine like terms: -5.25 + 0.75 = -4.5 t = -4.5 Simplifying t = -4.5Solution
The solution to the problem is based on the solutions from the subproblems. t = {6, -4.5}
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