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Simplifying 5s2 + -26s = 25 Reorder the terms: -26s + 5s2 = 25 Solving -26s + 5s2 = 25 Solving for variable 's'. Reorder the terms: -25 + -26s + 5s2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + -26s + 5s2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -5 + -5.2s + s2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -5.2s + 5 + s2 = 0 + 5 Reorder the terms: -5 + 5 + -5.2s + s2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -5.2s + s2 = 0 + 5 -5.2s + s2 = 0 + 5 Combine like terms: 0 + 5 = 5 -5.2s + s2 = 5 The s term is -5.2s. Take half its coefficient (-2.6). Square it (6.76) and add it to both sides. Add '6.76' to each side of the equation. -5.2s + 6.76 + s2 = 5 + 6.76 Reorder the terms: 6.76 + -5.2s + s2 = 5 + 6.76 Combine like terms: 5 + 6.76 = 11.76 6.76 + -5.2s + s2 = 11.76 Factor a perfect square on the left side: (s + -2.6)(s + -2.6) = 11.76 Calculate the square root of the right side: 3.42928564 Break this problem into two subproblems by setting (s + -2.6) equal to 3.42928564 and -3.42928564.Subproblem 1
s + -2.6 = 3.42928564 Simplifying s + -2.6 = 3.42928564 Reorder the terms: -2.6 + s = 3.42928564 Solving -2.6 + s = 3.42928564 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + s = 3.42928564 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + s = 3.42928564 + 2.6 s = 3.42928564 + 2.6 Combine like terms: 3.42928564 + 2.6 = 6.02928564 s = 6.02928564 Simplifying s = 6.02928564Subproblem 2
s + -2.6 = -3.42928564 Simplifying s + -2.6 = -3.42928564 Reorder the terms: -2.6 + s = -3.42928564 Solving -2.6 + s = -3.42928564 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + s = -3.42928564 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + s = -3.42928564 + 2.6 s = -3.42928564 + 2.6 Combine like terms: -3.42928564 + 2.6 = -0.82928564 s = -0.82928564 Simplifying s = -0.82928564Solution
The solution to the problem is based on the solutions from the subproblems. s = {6.02928564, -0.82928564}
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