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Simplifying t2 + -25t + 64 = 0 Reorder the terms: 64 + -25t + t2 = 0 Solving 64 + -25t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-64' to each side of the equation. 64 + -25t + -64 + t2 = 0 + -64 Reorder the terms: 64 + -64 + -25t + t2 = 0 + -64 Combine like terms: 64 + -64 = 0 0 + -25t + t2 = 0 + -64 -25t + t2 = 0 + -64 Combine like terms: 0 + -64 = -64 -25t + t2 = -64 The t term is -25t. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25t + 156.25 + t2 = -64 + 156.25 Reorder the terms: 156.25 + -25t + t2 = -64 + 156.25 Combine like terms: -64 + 156.25 = 92.25 156.25 + -25t + t2 = 92.25 Factor a perfect square on the left side: (t + -12.5)(t + -12.5) = 92.25 Calculate the square root of the right side: 9.604686356 Break this problem into two subproblems by setting (t + -12.5) equal to 9.604686356 and -9.604686356.Subproblem 1
t + -12.5 = 9.604686356 Simplifying t + -12.5 = 9.604686356 Reorder the terms: -12.5 + t = 9.604686356 Solving -12.5 + t = 9.604686356 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + t = 9.604686356 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + t = 9.604686356 + 12.5 t = 9.604686356 + 12.5 Combine like terms: 9.604686356 + 12.5 = 22.104686356 t = 22.104686356 Simplifying t = 22.104686356Subproblem 2
t + -12.5 = -9.604686356 Simplifying t + -12.5 = -9.604686356 Reorder the terms: -12.5 + t = -9.604686356 Solving -12.5 + t = -9.604686356 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + t = -9.604686356 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + t = -9.604686356 + 12.5 t = -9.604686356 + 12.5 Combine like terms: -9.604686356 + 12.5 = 2.895313644 t = 2.895313644 Simplifying t = 2.895313644Solution
The solution to the problem is based on the solutions from the subproblems. t = {22.104686356, 2.895313644}
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