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Simplifying x2 + 10x = 228 Reorder the terms: 10x + x2 = 228 Solving 10x + x2 = 228 Solving for variable 'x'. Reorder the terms: -228 + 10x + x2 = 228 + -228 Combine like terms: 228 + -228 = 0 -228 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '228' to each side of the equation. -228 + 10x + 228 + x2 = 0 + 228 Reorder the terms: -228 + 228 + 10x + x2 = 0 + 228 Combine like terms: -228 + 228 = 0 0 + 10x + x2 = 0 + 228 10x + x2 = 0 + 228 Combine like terms: 0 + 228 = 228 10x + x2 = 228 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 228 + 25 Reorder the terms: 25 + 10x + x2 = 228 + 25 Combine like terms: 228 + 25 = 253 25 + 10x + x2 = 253 Factor a perfect square on the left side: (x + 5)(x + 5) = 253 Calculate the square root of the right side: 15.905973721 Break this problem into two subproblems by setting (x + 5) equal to 15.905973721 and -15.905973721.Subproblem 1
x + 5 = 15.905973721 Simplifying x + 5 = 15.905973721 Reorder the terms: 5 + x = 15.905973721 Solving 5 + x = 15.905973721 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 15.905973721 + -5 Combine like terms: 5 + -5 = 0 0 + x = 15.905973721 + -5 x = 15.905973721 + -5 Combine like terms: 15.905973721 + -5 = 10.905973721 x = 10.905973721 Simplifying x = 10.905973721Subproblem 2
x + 5 = -15.905973721 Simplifying x + 5 = -15.905973721 Reorder the terms: 5 + x = -15.905973721 Solving 5 + x = -15.905973721 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -15.905973721 + -5 Combine like terms: 5 + -5 = 0 0 + x = -15.905973721 + -5 x = -15.905973721 + -5 Combine like terms: -15.905973721 + -5 = -20.905973721 x = -20.905973721 Simplifying x = -20.905973721Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.905973721, -20.905973721}
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