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Simplifying 5s2 + -17s = 6 Reorder the terms: -17s + 5s2 = 6 Solving -17s + 5s2 = 6 Solving for variable 's'. Reorder the terms: -6 + -17s + 5s2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + -17s + 5s2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.2 + -3.4s + s2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + -3.4s + 1.2 + s2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + -3.4s + s2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + -3.4s + s2 = 0 + 1.2 -3.4s + s2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 -3.4s + s2 = 1.2 The s term is -3.4s. Take half its coefficient (-1.7). Square it (2.89) and add it to both sides. Add '2.89' to each side of the equation. -3.4s + 2.89 + s2 = 1.2 + 2.89 Reorder the terms: 2.89 + -3.4s + s2 = 1.2 + 2.89 Combine like terms: 1.2 + 2.89 = 4.09 2.89 + -3.4s + s2 = 4.09 Factor a perfect square on the left side: (s + -1.7)(s + -1.7) = 4.09 Calculate the square root of the right side: 2.022374842 Break this problem into two subproblems by setting (s + -1.7) equal to 2.022374842 and -2.022374842.Subproblem 1
s + -1.7 = 2.022374842 Simplifying s + -1.7 = 2.022374842 Reorder the terms: -1.7 + s = 2.022374842 Solving -1.7 + s = 2.022374842 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + s = 2.022374842 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + s = 2.022374842 + 1.7 s = 2.022374842 + 1.7 Combine like terms: 2.022374842 + 1.7 = 3.722374842 s = 3.722374842 Simplifying s = 3.722374842Subproblem 2
s + -1.7 = -2.022374842 Simplifying s + -1.7 = -2.022374842 Reorder the terms: -1.7 + s = -2.022374842 Solving -1.7 + s = -2.022374842 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + s = -2.022374842 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + s = -2.022374842 + 1.7 s = -2.022374842 + 1.7 Combine like terms: -2.022374842 + 1.7 = -0.322374842 s = -0.322374842 Simplifying s = -0.322374842Solution
The solution to the problem is based on the solutions from the subproblems. s = {3.722374842, -0.322374842}
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