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Simplifying t2 + -0.5t + -14 = 0 Reorder the terms: -14 + -0.5t + t2 = 0 Solving -14 + -0.5t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + -0.5t + 14 + t2 = 0 + 14 Reorder the terms: -14 + 14 + -0.5t + t2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -0.5t + t2 = 0 + 14 -0.5t + t2 = 0 + 14 Combine like terms: 0 + 14 = 14 -0.5t + t2 = 14 The t term is -0.5t. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5t + 0.0625 + t2 = 14 + 0.0625 Reorder the terms: 0.0625 + -0.5t + t2 = 14 + 0.0625 Combine like terms: 14 + 0.0625 = 14.0625 0.0625 + -0.5t + t2 = 14.0625 Factor a perfect square on the left side: (t + -0.25)(t + -0.25) = 14.0625 Calculate the square root of the right side: 3.75 Break this problem into two subproblems by setting (t + -0.25) equal to 3.75 and -3.75.Subproblem 1
t + -0.25 = 3.75 Simplifying t + -0.25 = 3.75 Reorder the terms: -0.25 + t = 3.75 Solving -0.25 + t = 3.75 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + t = 3.75 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + t = 3.75 + 0.25 t = 3.75 + 0.25 Combine like terms: 3.75 + 0.25 = 4 t = 4 Simplifying t = 4Subproblem 2
t + -0.25 = -3.75 Simplifying t + -0.25 = -3.75 Reorder the terms: -0.25 + t = -3.75 Solving -0.25 + t = -3.75 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + t = -3.75 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + t = -3.75 + 0.25 t = -3.75 + 0.25 Combine like terms: -3.75 + 0.25 = -3.5 t = -3.5 Simplifying t = -3.5Solution
The solution to the problem is based on the solutions from the subproblems. t = {4, -3.5}
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