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Simplifying t2 + -24t + 125 = 0 Reorder the terms: 125 + -24t + t2 = 0 Solving 125 + -24t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-125' to each side of the equation. 125 + -24t + -125 + t2 = 0 + -125 Reorder the terms: 125 + -125 + -24t + t2 = 0 + -125 Combine like terms: 125 + -125 = 0 0 + -24t + t2 = 0 + -125 -24t + t2 = 0 + -125 Combine like terms: 0 + -125 = -125 -24t + t2 = -125 The t term is -24t. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24t + 144 + t2 = -125 + 144 Reorder the terms: 144 + -24t + t2 = -125 + 144 Combine like terms: -125 + 144 = 19 144 + -24t + t2 = 19 Factor a perfect square on the left side: (t + -12)(t + -12) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (t + -12) equal to 4.358898944 and -4.358898944.Subproblem 1
t + -12 = 4.358898944 Simplifying t + -12 = 4.358898944 Reorder the terms: -12 + t = 4.358898944 Solving -12 + t = 4.358898944 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + t = 4.358898944 + 12 Combine like terms: -12 + 12 = 0 0 + t = 4.358898944 + 12 t = 4.358898944 + 12 Combine like terms: 4.358898944 + 12 = 16.358898944 t = 16.358898944 Simplifying t = 16.358898944Subproblem 2
t + -12 = -4.358898944 Simplifying t + -12 = -4.358898944 Reorder the terms: -12 + t = -4.358898944 Solving -12 + t = -4.358898944 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + t = -4.358898944 + 12 Combine like terms: -12 + 12 = 0 0 + t = -4.358898944 + 12 t = -4.358898944 + 12 Combine like terms: -4.358898944 + 12 = 7.641101056 t = 7.641101056 Simplifying t = 7.641101056Solution
The solution to the problem is based on the solutions from the subproblems. t = {16.358898944, 7.641101056}
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