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Simplifying t2 + -12.5t + 25 = 0 Reorder the terms: 25 + -12.5t + t2 = 0 Solving 25 + -12.5t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + -12.5t + -25 + t2 = 0 + -25 Reorder the terms: 25 + -25 + -12.5t + t2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -12.5t + t2 = 0 + -25 -12.5t + t2 = 0 + -25 Combine like terms: 0 + -25 = -25 -12.5t + t2 = -25 The t term is -12.5t. Take half its coefficient (-6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. -12.5t + 39.0625 + t2 = -25 + 39.0625 Reorder the terms: 39.0625 + -12.5t + t2 = -25 + 39.0625 Combine like terms: -25 + 39.0625 = 14.0625 39.0625 + -12.5t + t2 = 14.0625 Factor a perfect square on the left side: (t + -6.25)(t + -6.25) = 14.0625 Calculate the square root of the right side: 3.75 Break this problem into two subproblems by setting (t + -6.25) equal to 3.75 and -3.75.Subproblem 1
t + -6.25 = 3.75 Simplifying t + -6.25 = 3.75 Reorder the terms: -6.25 + t = 3.75 Solving -6.25 + t = 3.75 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + t = 3.75 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + t = 3.75 + 6.25 t = 3.75 + 6.25 Combine like terms: 3.75 + 6.25 = 10 t = 10 Simplifying t = 10Subproblem 2
t + -6.25 = -3.75 Simplifying t + -6.25 = -3.75 Reorder the terms: -6.25 + t = -3.75 Solving -6.25 + t = -3.75 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + t = -3.75 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + t = -3.75 + 6.25 t = -3.75 + 6.25 Combine like terms: -3.75 + 6.25 = 2.5 t = 2.5 Simplifying t = 2.5Solution
The solution to the problem is based on the solutions from the subproblems. t = {10, 2.5}
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