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Simplifying 4s2 + 16s + 5 = 0 Reorder the terms: 5 + 16s + 4s2 = 0 Solving 5 + 16s + 4s2 = 0 Solving for variable 's'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + 4s + s2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + 4s + -1.25 + s2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + 4s + s2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + 4s + s2 = 0 + -1.25 4s + s2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 4s + s2 = -1.25 The s term is 4s. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4s + 4 + s2 = -1.25 + 4 Reorder the terms: 4 + 4s + s2 = -1.25 + 4 Combine like terms: -1.25 + 4 = 2.75 4 + 4s + s2 = 2.75 Factor a perfect square on the left side: (s + 2)(s + 2) = 2.75 Calculate the square root of the right side: 1.658312395 Break this problem into two subproblems by setting (s + 2) equal to 1.658312395 and -1.658312395.Subproblem 1
s + 2 = 1.658312395 Simplifying s + 2 = 1.658312395 Reorder the terms: 2 + s = 1.658312395 Solving 2 + s = 1.658312395 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + s = 1.658312395 + -2 Combine like terms: 2 + -2 = 0 0 + s = 1.658312395 + -2 s = 1.658312395 + -2 Combine like terms: 1.658312395 + -2 = -0.341687605 s = -0.341687605 Simplifying s = -0.341687605Subproblem 2
s + 2 = -1.658312395 Simplifying s + 2 = -1.658312395 Reorder the terms: 2 + s = -1.658312395 Solving 2 + s = -1.658312395 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + s = -1.658312395 + -2 Combine like terms: 2 + -2 = 0 0 + s = -1.658312395 + -2 s = -1.658312395 + -2 Combine like terms: -1.658312395 + -2 = -3.658312395 s = -3.658312395 Simplifying s = -3.658312395Solution
The solution to the problem is based on the solutions from the subproblems. s = {-0.341687605, -3.658312395}
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