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Simplifying (X2) + X + -234 = 0 X2 + X + -234 = 0 Reorder the terms: -234 + X + X2 = 0 Solving -234 + X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '234' to each side of the equation. -234 + X + 234 + X2 = 0 + 234 Reorder the terms: -234 + 234 + X + X2 = 0 + 234 Combine like terms: -234 + 234 = 0 0 + X + X2 = 0 + 234 X + X2 = 0 + 234 Combine like terms: 0 + 234 = 234 X + X2 = 234 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 = 234 + 0.25 Reorder the terms: 0.25 + X + X2 = 234 + 0.25 Combine like terms: 234 + 0.25 = 234.25 0.25 + X + X2 = 234.25 Factor a perfect square on the left side: (X + 0.5)(X + 0.5) = 234.25 Calculate the square root of the right side: 15.305227865 Break this problem into two subproblems by setting (X + 0.5) equal to 15.305227865 and -15.305227865.Subproblem 1
X + 0.5 = 15.305227865 Simplifying X + 0.5 = 15.305227865 Reorder the terms: 0.5 + X = 15.305227865 Solving 0.5 + X = 15.305227865 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 = 15.305227865 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = 15.305227865 + -0.5 X = 15.305227865 + -0.5 Combine like terms: 15.305227865 + -0.5 = 14.805227865 X = 14.805227865 Simplifying X = 14.805227865Subproblem 2
X + 0.5 = -15.305227865 Simplifying X + 0.5 = -15.305227865 Reorder the terms: 0.5 + X = -15.305227865 Solving 0.5 + X = -15.305227865 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 = -15.305227865 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = -15.305227865 + -0.5 X = -15.305227865 + -0.5 Combine like terms: -15.305227865 + -0.5 = -15.805227865 X = -15.805227865 Simplifying X = -15.805227865Solution
The solution to the problem is based on the solutions from the subproblems. X = {14.805227865, -15.805227865}
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