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Simplifying 5s2 + -10s = 23 Reorder the terms: -10s + 5s2 = 23 Solving -10s + 5s2 = 23 Solving for variable 's'. Reorder the terms: -23 + -10s + 5s2 = 23 + -23 Combine like terms: 23 + -23 = 0 -23 + -10s + 5s2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.6 + -2s + s2 = 0 Move the constant term to the right: Add '4.6' to each side of the equation. -4.6 + -2s + 4.6 + s2 = 0 + 4.6 Reorder the terms: -4.6 + 4.6 + -2s + s2 = 0 + 4.6 Combine like terms: -4.6 + 4.6 = 0.0 0.0 + -2s + s2 = 0 + 4.6 -2s + s2 = 0 + 4.6 Combine like terms: 0 + 4.6 = 4.6 -2s + s2 = 4.6 The s term is -2s. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2s + 1 + s2 = 4.6 + 1 Reorder the terms: 1 + -2s + s2 = 4.6 + 1 Combine like terms: 4.6 + 1 = 5.6 1 + -2s + s2 = 5.6 Factor a perfect square on the left side: (s + -1)(s + -1) = 5.6 Calculate the square root of the right side: 2.366431913 Break this problem into two subproblems by setting (s + -1) equal to 2.366431913 and -2.366431913.Subproblem 1
s + -1 = 2.366431913 Simplifying s + -1 = 2.366431913 Reorder the terms: -1 + s = 2.366431913 Solving -1 + s = 2.366431913 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + s = 2.366431913 + 1 Combine like terms: -1 + 1 = 0 0 + s = 2.366431913 + 1 s = 2.366431913 + 1 Combine like terms: 2.366431913 + 1 = 3.366431913 s = 3.366431913 Simplifying s = 3.366431913Subproblem 2
s + -1 = -2.366431913 Simplifying s + -1 = -2.366431913 Reorder the terms: -1 + s = -2.366431913 Solving -1 + s = -2.366431913 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + s = -2.366431913 + 1 Combine like terms: -1 + 1 = 0 0 + s = -2.366431913 + 1 s = -2.366431913 + 1 Combine like terms: -2.366431913 + 1 = -1.366431913 s = -1.366431913 Simplifying s = -1.366431913Solution
The solution to the problem is based on the solutions from the subproblems. s = {3.366431913, -1.366431913}
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