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Simplifying t2 + -14t + -21 = 0 Reorder the terms: -21 + -14t + t2 = 0 Solving -21 + -14t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + -14t + 21 + t2 = 0 + 21 Reorder the terms: -21 + 21 + -14t + t2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -14t + t2 = 0 + 21 -14t + t2 = 0 + 21 Combine like terms: 0 + 21 = 21 -14t + t2 = 21 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 = 21 + 49 Reorder the terms: 49 + -14t + t2 = 21 + 49 Combine like terms: 21 + 49 = 70 49 + -14t + t2 = 70 Factor a perfect square on the left side: (t + -7)(t + -7) = 70 Calculate the square root of the right side: 8.366600265 Break this problem into two subproblems by setting (t + -7) equal to 8.366600265 and -8.366600265.Subproblem 1
t + -7 = 8.366600265 Simplifying t + -7 = 8.366600265 Reorder the terms: -7 + t = 8.366600265 Solving -7 + t = 8.366600265 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 = 8.366600265 + 7 Combine like terms: -7 + 7 = 0 0 + t = 8.366600265 + 7 t = 8.366600265 + 7 Combine like terms: 8.366600265 + 7 = 15.366600265 t = 15.366600265 Simplifying t = 15.366600265Subproblem 2
t + -7 = -8.366600265 Simplifying t + -7 = -8.366600265 Reorder the terms: -7 + t = -8.366600265 Solving -7 + t = -8.366600265 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 = -8.366600265 + 7 Combine like terms: -7 + 7 = 0 0 + t = -8.366600265 + 7 t = -8.366600265 + 7 Combine like terms: -8.366600265 + 7 = -1.366600265 t = -1.366600265 Simplifying t = -1.366600265Solution
The solution to the problem is based on the solutions from the subproblems. t = {15.366600265, -1.366600265}
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