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Simplifying 4s + s2 = 15 Solving 4s + s2 = 15 Solving for variable 's'. Reorder the terms: -15 + 4s + s2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + 4s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 4s + 15 + s2 = 0 + 15 Reorder the terms: -15 + 15 + 4s + s2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 4s + s2 = 0 + 15 4s + s2 = 0 + 15 Combine like terms: 0 + 15 = 15 4s + s2 = 15 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 = 15 + 4 Reorder the terms: 4 + 4s + s2 = 15 + 4 Combine like terms: 15 + 4 = 19 4 + 4s + s2 = 19 Factor a perfect square on the left side: (s + 2)(s + 2) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (s + 2) equal to 4.358898944 and -4.358898944.Subproblem 1
s + 2 = 4.358898944 Simplifying s + 2 = 4.358898944 Reorder the terms: 2 + s = 4.358898944 Solving 2 + s = 4.358898944 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 = 4.358898944 + -2 Combine like terms: 2 + -2 = 0 0 + s = 4.358898944 + -2 s = 4.358898944 + -2 Combine like terms: 4.358898944 + -2 = 2.358898944 s = 2.358898944 Simplifying s = 2.358898944Subproblem 2
s + 2 = -4.358898944 Simplifying s + 2 = -4.358898944 Reorder the terms: 2 + s = -4.358898944 Solving 2 + s = -4.358898944 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 = -4.358898944 + -2 Combine like terms: 2 + -2 = 0 0 + s = -4.358898944 + -2 s = -4.358898944 + -2 Combine like terms: -4.358898944 + -2 = -6.358898944 s = -6.358898944 Simplifying s = -6.358898944Solution
The solution to the problem is based on the solutions from the subproblems. s = {2.358898944, -6.358898944}
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