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Simplifying x2 + -57x + 216 = 0 Reorder the terms: 216 + -57x + x2 = 0 Solving 216 + -57x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-216' to each side of the equation. 216 + -57x + -216 + x2 = 0 + -216 Reorder the terms: 216 + -216 + -57x + x2 = 0 + -216 Combine like terms: 216 + -216 = 0 0 + -57x + x2 = 0 + -216 -57x + x2 = 0 + -216 Combine like terms: 0 + -216 = -216 -57x + x2 = -216 The x term is -57x. Take half its coefficient (-28.5). Square it (812.25) and add it to both sides. Add '812.25' to each side of the equation. -57x + 812.25 + x2 = -216 + 812.25 Reorder the terms: 812.25 + -57x + x2 = -216 + 812.25 Combine like terms: -216 + 812.25 = 596.25 812.25 + -57x + x2 = 596.25 Factor a perfect square on the left side: (x + -28.5)(x + -28.5) = 596.25 Calculate the square root of the right side: 24.418230894 Break this problem into two subproblems by setting (x + -28.5) equal to 24.418230894 and -24.418230894.Subproblem 1
x + -28.5 = 24.418230894 Simplifying x + -28.5 = 24.418230894 Reorder the terms: -28.5 + x = 24.418230894 Solving -28.5 + x = 24.418230894 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '28.5' to each side of the equation. -28.5 + 28.5 + x = 24.418230894 + 28.5 Combine like terms: -28.5 + 28.5 = 0.0 0.0 + x = 24.418230894 + 28.5 x = 24.418230894 + 28.5 Combine like terms: 24.418230894 + 28.5 = 52.918230894 x = 52.918230894 Simplifying x = 52.918230894Subproblem 2
x + -28.5 = -24.418230894 Simplifying x + -28.5 = -24.418230894 Reorder the terms: -28.5 + x = -24.418230894 Solving -28.5 + x = -24.418230894 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '28.5' to each side of the equation. -28.5 + 28.5 + x = -24.418230894 + 28.5 Combine like terms: -28.5 + 28.5 = 0.0 0.0 + x = -24.418230894 + 28.5 x = -24.418230894 + 28.5 Combine like terms: -24.418230894 + 28.5 = 4.081769106 x = 4.081769106 Simplifying x = 4.081769106Solution
The solution to the problem is based on the solutions from the subproblems. x = {52.918230894, 4.081769106}
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