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Simplifying s2 + -3(s + 3) = 4 Reorder the terms: s2 + -3(3 + s) = 4 s2 + (3 * -3 + s * -3) = 4 s2 + (-9 + -3s) = 4 Reorder the terms: -9 + -3s + s2 = 4 Solving -9 + -3s + s2 = 4 Solving for variable 's'. Reorder the terms: -9 + -4 + -3s + s2 = 4 + -4 Combine like terms: -9 + -4 = -13 -13 + -3s + s2 = 4 + -4 Combine like terms: 4 + -4 = 0 -13 + -3s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + -3s + 13 + s2 = 0 + 13 Reorder the terms: -13 + 13 + -3s + s2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -3s + s2 = 0 + 13 -3s + s2 = 0 + 13 Combine like terms: 0 + 13 = 13 -3s + s2 = 13 The s term is -3s. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3s + 2.25 + s2 = 13 + 2.25 Reorder the terms: 2.25 + -3s + s2 = 13 + 2.25 Combine like terms: 13 + 2.25 = 15.25 2.25 + -3s + s2 = 15.25 Factor a perfect square on the left side: (s + -1.5)(s + -1.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (s + -1.5) equal to 3.905124838 and -3.905124838.Subproblem 1
s + -1.5 = 3.905124838 Simplifying s + -1.5 = 3.905124838 Reorder the terms: -1.5 + s = 3.905124838 Solving -1.5 + s = 3.905124838 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + s = 3.905124838 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + s = 3.905124838 + 1.5 s = 3.905124838 + 1.5 Combine like terms: 3.905124838 + 1.5 = 5.405124838 s = 5.405124838 Simplifying s = 5.405124838Subproblem 2
s + -1.5 = -3.905124838 Simplifying s + -1.5 = -3.905124838 Reorder the terms: -1.5 + s = -3.905124838 Solving -1.5 + s = -3.905124838 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + s = -3.905124838 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + s = -3.905124838 + 1.5 s = -3.905124838 + 1.5 Combine like terms: -3.905124838 + 1.5 = -2.405124838 s = -2.405124838 Simplifying s = -2.405124838Solution
The solution to the problem is based on the solutions from the subproblems. s = {5.405124838, -2.405124838}
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