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Simplifying 5s2 + 1s + -12 = 0 Reorder the terms: -12 + 1s + 5s2 = 0 Solving -12 + 1s + 5s2 = 0 Solving for variable 's'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.4 + 0.2s + s2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + 0.2s + 2.4 + s2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + 0.2s + s2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + 0.2s + s2 = 0 + 2.4 0.2s + s2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 0.2s + s2 = 2.4 The s term is 0.2s. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2s + 0.01 + s2 = 2.4 + 0.01 Reorder the terms: 0.01 + 0.2s + s2 = 2.4 + 0.01 Combine like terms: 2.4 + 0.01 = 2.41 0.01 + 0.2s + s2 = 2.41 Factor a perfect square on the left side: (s + 0.1)(s + 0.1) = 2.41 Calculate the square root of the right side: 1.55241747 Break this problem into two subproblems by setting (s + 0.1) equal to 1.55241747 and -1.55241747.Subproblem 1
s + 0.1 = 1.55241747 Simplifying s + 0.1 = 1.55241747 Reorder the terms: 0.1 + s = 1.55241747 Solving 0.1 + s = 1.55241747 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + s = 1.55241747 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + s = 1.55241747 + -0.1 s = 1.55241747 + -0.1 Combine like terms: 1.55241747 + -0.1 = 1.45241747 s = 1.45241747 Simplifying s = 1.45241747Subproblem 2
s + 0.1 = -1.55241747 Simplifying s + 0.1 = -1.55241747 Reorder the terms: 0.1 + s = -1.55241747 Solving 0.1 + s = -1.55241747 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + s = -1.55241747 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + s = -1.55241747 + -0.1 s = -1.55241747 + -0.1 Combine like terms: -1.55241747 + -0.1 = -1.65241747 s = -1.65241747 Simplifying s = -1.65241747Solution
The solution to the problem is based on the solutions from the subproblems. s = {1.45241747, -1.65241747}
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