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Simplifying 7s2 + -8s + -8 = 0 Reorder the terms: -8 + -8s + 7s2 = 0 Solving -8 + -8s + 7s2 = 0 Solving for variable 's'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.142857143 + -1.142857143s + s2 = 0 Move the constant term to the right: Add '1.142857143' to each side of the equation. -1.142857143 + -1.142857143s + 1.142857143 + s2 = 0 + 1.142857143 Reorder the terms: -1.142857143 + 1.142857143 + -1.142857143s + s2 = 0 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + -1.142857143s + s2 = 0 + 1.142857143 -1.142857143s + s2 = 0 + 1.142857143 Combine like terms: 0 + 1.142857143 = 1.142857143 -1.142857143s + s2 = 1.142857143 The s term is -1.142857143s. Take half its coefficient (-0.5714285715). Square it (0.3265306123) and add it to both sides. Add '0.3265306123' to each side of the equation. -1.142857143s + 0.3265306123 + s2 = 1.142857143 + 0.3265306123 Reorder the terms: 0.3265306123 + -1.142857143s + s2 = 1.142857143 + 0.3265306123 Combine like terms: 1.142857143 + 0.3265306123 = 1.4693877553 0.3265306123 + -1.142857143s + s2 = 1.4693877553 Factor a perfect square on the left side: (s + -0.5714285715)(s + -0.5714285715) = 1.4693877553 Calculate the square root of the right side: 1.212183054 Break this problem into two subproblems by setting (s + -0.5714285715) equal to 1.212183054 and -1.212183054.Subproblem 1
s + -0.5714285715 = 1.212183054 Simplifying s + -0.5714285715 = 1.212183054 Reorder the terms: -0.5714285715 + s = 1.212183054 Solving -0.5714285715 + s = 1.212183054 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.5714285715' to each side of the equation. -0.5714285715 + 0.5714285715 + s = 1.212183054 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + s = 1.212183054 + 0.5714285715 s = 1.212183054 + 0.5714285715 Combine like terms: 1.212183054 + 0.5714285715 = 1.7836116255 s = 1.7836116255 Simplifying s = 1.7836116255Subproblem 2
s + -0.5714285715 = -1.212183054 Simplifying s + -0.5714285715 = -1.212183054 Reorder the terms: -0.5714285715 + s = -1.212183054 Solving -0.5714285715 + s = -1.212183054 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.5714285715' to each side of the equation. -0.5714285715 + 0.5714285715 + s = -1.212183054 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + s = -1.212183054 + 0.5714285715 s = -1.212183054 + 0.5714285715 Combine like terms: -1.212183054 + 0.5714285715 = -0.6407544825 s = -0.6407544825 Simplifying s = -0.6407544825Solution
The solution to the problem is based on the solutions from the subproblems. s = {1.7836116255, -0.6407544825}
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