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Simplifying t2 = 14t + 24 Reorder the terms: t2 = 24 + 14t Solving t2 = 24 + 14t Solving for variable 't'. Reorder the terms: -24 + -14t + t2 = 24 + 14t + -24 + -14t Reorder the terms: -24 + -14t + t2 = 24 + -24 + 14t + -14t Combine like terms: 24 + -24 = 0 -24 + -14t + t2 = 0 + 14t + -14t -24 + -14t + t2 = 14t + -14t Combine like terms: 14t + -14t = 0 -24 + -14t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + -14t + 24 + t2 = 0 + 24 Reorder the terms: -24 + 24 + -14t + t2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -14t + t2 = 0 + 24 -14t + t2 = 0 + 24 Combine like terms: 0 + 24 = 24 -14t + t2 = 24 The t term is -14t. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14t + 49 + t2 = 24 + 49 Reorder the terms: 49 + -14t + t2 = 24 + 49 Combine like terms: 24 + 49 = 73 49 + -14t + t2 = 73 Factor a perfect square on the left side: (t + -7)(t + -7) = 73 Calculate the square root of the right side: 8.544003745 Break this problem into two subproblems by setting (t + -7) equal to 8.544003745 and -8.544003745.Subproblem 1
t + -7 = 8.544003745 Simplifying t + -7 = 8.544003745 Reorder the terms: -7 + t = 8.544003745 Solving -7 + t = 8.544003745 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + t = 8.544003745 + 7 Combine like terms: -7 + 7 = 0 0 + t = 8.544003745 + 7 t = 8.544003745 + 7 Combine like terms: 8.544003745 + 7 = 15.544003745 t = 15.544003745 Simplifying t = 15.544003745Subproblem 2
t + -7 = -8.544003745 Simplifying t + -7 = -8.544003745 Reorder the terms: -7 + t = -8.544003745 Solving -7 + t = -8.544003745 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + t = -8.544003745 + 7 Combine like terms: -7 + 7 = 0 0 + t = -8.544003745 + 7 t = -8.544003745 + 7 Combine like terms: -8.544003745 + 7 = -1.544003745 t = -1.544003745 Simplifying t = -1.544003745Solution
The solution to the problem is based on the solutions from the subproblems. t = {15.544003745, -1.544003745}
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