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Simplifying 5s2 + -5s + -7 = 0 Reorder the terms: -7 + -5s + 5s2 = 0 Solving -7 + -5s + 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'. -1.4 + -1s + s2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + -1s + 1.4 + s2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + -1s + s2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + -1s + s2 = 0 + 1.4 -1s + s2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 -1s + s2 = 1.4 The s term is -1s. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1s + 0.25 + s2 = 1.4 + 0.25 Reorder the terms: 0.25 + -1s + s2 = 1.4 + 0.25 Combine like terms: 1.4 + 0.25 = 1.65 0.25 + -1s + s2 = 1.65 Factor a perfect square on the left side: (s + -0.5)(s + -0.5) = 1.65 Calculate the square root of the right side: 1.284523258 Break this problem into two subproblems by setting (s + -0.5) equal to 1.284523258 and -1.284523258.Subproblem 1
s + -0.5 = 1.284523258 Simplifying s + -0.5 = 1.284523258 Reorder the terms: -0.5 + s = 1.284523258 Solving -0.5 + s = 1.284523258 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + s = 1.284523258 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + s = 1.284523258 + 0.5 s = 1.284523258 + 0.5 Combine like terms: 1.284523258 + 0.5 = 1.784523258 s = 1.784523258 Simplifying s = 1.784523258Subproblem 2
s + -0.5 = -1.284523258 Simplifying s + -0.5 = -1.284523258 Reorder the terms: -0.5 + s = -1.284523258 Solving -0.5 + s = -1.284523258 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + s = -1.284523258 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + s = -1.284523258 + 0.5 s = -1.284523258 + 0.5 Combine like terms: -1.284523258 + 0.5 = -0.784523258 s = -0.784523258 Simplifying s = -0.784523258Solution
The solution to the problem is based on the solutions from the subproblems. s = {1.784523258, -0.784523258}
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