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Simplifying 7s2 + 9s + -4 = 0 Reorder the terms: -4 + 9s + 7s2 = 0 Solving -4 + 9s + 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'. -0.5714285714 + 1.285714286s + s2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + 1.285714286s + 0.5714285714 + s2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + 1.285714286s + s2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + 1.285714286s + s2 = 0 + 0.5714285714 1.285714286s + s2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 1.285714286s + s2 = 0.5714285714 The s term is 1.285714286s. Take half its coefficient (0.642857143). Square it (0.4132653063) and add it to both sides. Add '0.4132653063' to each side of the equation. 1.285714286s + 0.4132653063 + s2 = 0.5714285714 + 0.4132653063 Reorder the terms: 0.4132653063 + 1.285714286s + s2 = 0.5714285714 + 0.4132653063 Combine like terms: 0.5714285714 + 0.4132653063 = 0.9846938777 0.4132653063 + 1.285714286s + s2 = 0.9846938777 Factor a perfect square on the left side: (s + 0.642857143)(s + 0.642857143) = 0.9846938777 Calculate the square root of the right side: 0.992317428 Break this problem into two subproblems by setting (s + 0.642857143) equal to 0.992317428 and -0.992317428.Subproblem 1
s + 0.642857143 = 0.992317428 Simplifying s + 0.642857143 = 0.992317428 Reorder the terms: 0.642857143 + s = 0.992317428 Solving 0.642857143 + s = 0.992317428 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.642857143' to each side of the equation. 0.642857143 + -0.642857143 + s = 0.992317428 + -0.642857143 Combine like terms: 0.642857143 + -0.642857143 = 0.000000000 0.000000000 + s = 0.992317428 + -0.642857143 s = 0.992317428 + -0.642857143 Combine like terms: 0.992317428 + -0.642857143 = 0.349460285 s = 0.349460285 Simplifying s = 0.349460285Subproblem 2
s + 0.642857143 = -0.992317428 Simplifying s + 0.642857143 = -0.992317428 Reorder the terms: 0.642857143 + s = -0.992317428 Solving 0.642857143 + s = -0.992317428 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.642857143' to each side of the equation. 0.642857143 + -0.642857143 + s = -0.992317428 + -0.642857143 Combine like terms: 0.642857143 + -0.642857143 = 0.000000000 0.000000000 + s = -0.992317428 + -0.642857143 s = -0.992317428 + -0.642857143 Combine like terms: -0.992317428 + -0.642857143 = -1.635174571 s = -1.635174571 Simplifying s = -1.635174571Solution
The solution to the problem is based on the solutions from the subproblems. s = {0.349460285, -1.635174571}
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