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Simplifying t2 + -24t + -14 = 0 Reorder the terms: -14 + -24t + t2 = 0 Solving -14 + -24t + 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 + -24t + 14 + t2 = 0 + 14 Reorder the terms: -14 + 14 + -24t + t2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -24t + t2 = 0 + 14 -24t + t2 = 0 + 14 Combine like terms: 0 + 14 = 14 -24t + t2 = 14 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 = 14 + 144 Reorder the terms: 144 + -24t + t2 = 14 + 144 Combine like terms: 14 + 144 = 158 144 + -24t + t2 = 158 Factor a perfect square on the left side: (t + -12)(t + -12) = 158 Calculate the square root of the right side: 12.56980509 Break this problem into two subproblems by setting (t + -12) equal to 12.56980509 and -12.56980509.Subproblem 1
t + -12 = 12.56980509 Simplifying t + -12 = 12.56980509 Reorder the terms: -12 + t = 12.56980509 Solving -12 + t = 12.56980509 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 = 12.56980509 + 12 Combine like terms: -12 + 12 = 0 0 + t = 12.56980509 + 12 t = 12.56980509 + 12 Combine like terms: 12.56980509 + 12 = 24.56980509 t = 24.56980509 Simplifying t = 24.56980509Subproblem 2
t + -12 = -12.56980509 Simplifying t + -12 = -12.56980509 Reorder the terms: -12 + t = -12.56980509 Solving -12 + t = -12.56980509 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 = -12.56980509 + 12 Combine like terms: -12 + 12 = 0 0 + t = -12.56980509 + 12 t = -12.56980509 + 12 Combine like terms: -12.56980509 + 12 = -0.56980509 t = -0.56980509 Simplifying t = -0.56980509Solution
The solution to the problem is based on the solutions from the subproblems. t = {24.56980509, -0.56980509}
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