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Simplifying -8s2 + 4s + 1 = 0 Reorder the terms: 1 + 4s + -8s2 = 0 Solving 1 + 4s + -8s2 = 0 Solving for variable 's'. Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.125 + -0.5s + s2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -0.5s + 0.125 + s2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -0.5s + s2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -0.5s + s2 = 0 + 0.125 -0.5s + s2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -0.5s + s2 = 0.125 The s term is -0.5s. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5s + 0.0625 + s2 = 0.125 + 0.0625 Reorder the terms: 0.0625 + -0.5s + s2 = 0.125 + 0.0625 Combine like terms: 0.125 + 0.0625 = 0.1875 0.0625 + -0.5s + s2 = 0.1875 Factor a perfect square on the left side: (s + -0.25)(s + -0.25) = 0.1875 Calculate the square root of the right side: 0.433012702 Break this problem into two subproblems by setting (s + -0.25) equal to 0.433012702 and -0.433012702.Subproblem 1
s + -0.25 = 0.433012702 Simplifying s + -0.25 = 0.433012702 Reorder the terms: -0.25 + s = 0.433012702 Solving -0.25 + s = 0.433012702 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + s = 0.433012702 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + s = 0.433012702 + 0.25 s = 0.433012702 + 0.25 Combine like terms: 0.433012702 + 0.25 = 0.683012702 s = 0.683012702 Simplifying s = 0.683012702Subproblem 2
s + -0.25 = -0.433012702 Simplifying s + -0.25 = -0.433012702 Reorder the terms: -0.25 + s = -0.433012702 Solving -0.25 + s = -0.433012702 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + s = -0.433012702 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + s = -0.433012702 + 0.25 s = -0.433012702 + 0.25 Combine like terms: -0.433012702 + 0.25 = -0.183012702 s = -0.183012702 Simplifying s = -0.183012702Solution
The solution to the problem is based on the solutions from the subproblems. s = {0.683012702, -0.183012702}
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