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Simplifying t2 + 1.5t + -22 = 0 Reorder the terms: -22 + 1.5t + t2 = 0 Solving -22 + 1.5t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + 1.5t + 22 + t2 = 0 + 22 Reorder the terms: -22 + 22 + 1.5t + t2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + 1.5t + t2 = 0 + 22 1.5t + t2 = 0 + 22 Combine like terms: 0 + 22 = 22 1.5t + t2 = 22 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 = 22 + 0.5625 Reorder the terms: 0.5625 + 1.5t + t2 = 22 + 0.5625 Combine like terms: 22 + 0.5625 = 22.5625 0.5625 + 1.5t + t2 = 22.5625 Factor a perfect square on the left side: (t + 0.75)(t + 0.75) = 22.5625 Calculate the square root of the right side: 4.75 Break this problem into two subproblems by setting (t + 0.75) equal to 4.75 and -4.75.Subproblem 1
t + 0.75 = 4.75 Simplifying t + 0.75 = 4.75 Reorder the terms: 0.75 + t = 4.75 Solving 0.75 + t = 4.75 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 = 4.75 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + t = 4.75 + -0.75 t = 4.75 + -0.75 Combine like terms: 4.75 + -0.75 = 4 t = 4 Simplifying t = 4Subproblem 2
t + 0.75 = -4.75 Simplifying t + 0.75 = -4.75 Reorder the terms: 0.75 + t = -4.75 Solving 0.75 + t = -4.75 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 = -4.75 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + t = -4.75 + -0.75 t = -4.75 + -0.75 Combine like terms: -4.75 + -0.75 = -5.5 t = -5.5 Simplifying t = -5.5Solution
The solution to the problem is based on the solutions from the subproblems. t = {4, -5.5}
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