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Simplifying t2 + -21t + -126 = 0 Reorder the terms: -126 + -21t + t2 = 0 Solving -126 + -21t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '126' to each side of the equation. -126 + -21t + 126 + t2 = 0 + 126 Reorder the terms: -126 + 126 + -21t + t2 = 0 + 126 Combine like terms: -126 + 126 = 0 0 + -21t + t2 = 0 + 126 -21t + t2 = 0 + 126 Combine like terms: 0 + 126 = 126 -21t + t2 = 126 The t term is -21t. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21t + 110.25 + t2 = 126 + 110.25 Reorder the terms: 110.25 + -21t + t2 = 126 + 110.25 Combine like terms: 126 + 110.25 = 236.25 110.25 + -21t + t2 = 236.25 Factor a perfect square on the left side: (t + -10.5)(t + -10.5) = 236.25 Calculate the square root of the right side: 15.370426149 Break this problem into two subproblems by setting (t + -10.5) equal to 15.370426149 and -15.370426149.Subproblem 1
t + -10.5 = 15.370426149 Simplifying t + -10.5 = 15.370426149 Reorder the terms: -10.5 + t = 15.370426149 Solving -10.5 + t = 15.370426149 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + t = 15.370426149 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + t = 15.370426149 + 10.5 t = 15.370426149 + 10.5 Combine like terms: 15.370426149 + 10.5 = 25.870426149 t = 25.870426149 Simplifying t = 25.870426149Subproblem 2
t + -10.5 = -15.370426149 Simplifying t + -10.5 = -15.370426149 Reorder the terms: -10.5 + t = -15.370426149 Solving -10.5 + t = -15.370426149 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + t = -15.370426149 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + t = -15.370426149 + 10.5 t = -15.370426149 + 10.5 Combine like terms: -15.370426149 + 10.5 = -4.870426149 t = -4.870426149 Simplifying t = -4.870426149Solution
The solution to the problem is based on the solutions from the subproblems. t = {25.870426149, -4.870426149}
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