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Simplifying S2 + -4S = 30 Reorder the terms: -4S + S2 = 30 Solving -4S + S2 = 30 Solving for variable 'S'. Reorder the terms: -30 + -4S + S2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + -4S + S2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + -4S + 30 + S2 = 0 + 30 Reorder the terms: -30 + 30 + -4S + S2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -4S + S2 = 0 + 30 -4S + S2 = 0 + 30 Combine like terms: 0 + 30 = 30 -4S + S2 = 30 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 = 30 + 4 Reorder the terms: 4 + -4S + S2 = 30 + 4 Combine like terms: 30 + 4 = 34 4 + -4S + S2 = 34 Factor a perfect square on the left side: (S + -2)(S + -2) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (S + -2) equal to 5.830951895 and -5.830951895.Subproblem 1
S + -2 = 5.830951895 Simplifying S + -2 = 5.830951895 Reorder the terms: -2 + S = 5.830951895 Solving -2 + S = 5.830951895 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 = 5.830951895 + 2 Combine like terms: -2 + 2 = 0 0 + S = 5.830951895 + 2 S = 5.830951895 + 2 Combine like terms: 5.830951895 + 2 = 7.830951895 S = 7.830951895 Simplifying S = 7.830951895Subproblem 2
S + -2 = -5.830951895 Simplifying S + -2 = -5.830951895 Reorder the terms: -2 + S = -5.830951895 Solving -2 + S = -5.830951895 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 = -5.830951895 + 2 Combine like terms: -2 + 2 = 0 0 + S = -5.830951895 + 2 S = -5.830951895 + 2 Combine like terms: -5.830951895 + 2 = -3.830951895 S = -3.830951895 Simplifying S = -3.830951895Solution
The solution to the problem is based on the solutions from the subproblems. S = {7.830951895, -3.830951895}
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