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Simplifying x2 + x = 204 Reorder the terms: x + x2 = 204 Solving x + x2 = 204 Solving for variable 'x'. Reorder the terms: -204 + x + x2 = 204 + -204 Combine like terms: 204 + -204 = 0 -204 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '204' to each side of the equation. -204 + x + 204 + x2 = 0 + 204 Reorder the terms: -204 + 204 + x + x2 = 0 + 204 Combine like terms: -204 + 204 = 0 0 + x + x2 = 0 + 204 x + x2 = 0 + 204 Combine like terms: 0 + 204 = 204 x + x2 = 204 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 204 + 0.25 Reorder the terms: 0.25 + x + x2 = 204 + 0.25 Combine like terms: 204 + 0.25 = 204.25 0.25 + x + x2 = 204.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 204.25 Calculate the square root of the right side: 14.291605928 Break this problem into two subproblems by setting (x + 0.5) equal to 14.291605928 and -14.291605928.Subproblem 1
x + 0.5 = 14.291605928 Simplifying x + 0.5 = 14.291605928 Reorder the terms: 0.5 + x = 14.291605928 Solving 0.5 + x = 14.291605928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 14.291605928 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 14.291605928 + -0.5 x = 14.291605928 + -0.5 Combine like terms: 14.291605928 + -0.5 = 13.791605928 x = 13.791605928 Simplifying x = 13.791605928Subproblem 2
x + 0.5 = -14.291605928 Simplifying x + 0.5 = -14.291605928 Reorder the terms: 0.5 + x = -14.291605928 Solving 0.5 + x = -14.291605928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -14.291605928 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -14.291605928 + -0.5 x = -14.291605928 + -0.5 Combine like terms: -14.291605928 + -0.5 = -14.791605928 x = -14.791605928 Simplifying x = -14.791605928Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.791605928, -14.791605928}
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