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Simplifying X2 + X = 9434 Reorder the terms: X + X2 = 9434 Solving X + X2 = 9434 Solving for variable 'X'. Reorder the terms: -9434 + X + X2 = 9434 + -9434 Combine like terms: 9434 + -9434 = 0 -9434 + X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '9434' to each side of the equation. -9434 + X + 9434 + X2 = 0 + 9434 Reorder the terms: -9434 + 9434 + X + X2 = 0 + 9434 Combine like terms: -9434 + 9434 = 0 0 + X + X2 = 0 + 9434 X + X2 = 0 + 9434 Combine like terms: 0 + 9434 = 9434 X + X2 = 9434 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 = 9434 + 0.25 Reorder the terms: 0.25 + X + X2 = 9434 + 0.25 Combine like terms: 9434 + 0.25 = 9434.25 0.25 + X + X2 = 9434.25 Factor a perfect square on the left side: (X + 0.5)(X + 0.5) = 9434.25 Calculate the square root of the right side: 97.130067435 Break this problem into two subproblems by setting (X + 0.5) equal to 97.130067435 and -97.130067435.Subproblem 1
X + 0.5 = 97.130067435 Simplifying X + 0.5 = 97.130067435 Reorder the terms: 0.5 + X = 97.130067435 Solving 0.5 + X = 97.130067435 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 = 97.130067435 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = 97.130067435 + -0.5 X = 97.130067435 + -0.5 Combine like terms: 97.130067435 + -0.5 = 96.630067435 X = 96.630067435 Simplifying X = 96.630067435Subproblem 2
X + 0.5 = -97.130067435 Simplifying X + 0.5 = -97.130067435 Reorder the terms: 0.5 + X = -97.130067435 Solving 0.5 + X = -97.130067435 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 = -97.130067435 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = -97.130067435 + -0.5 X = -97.130067435 + -0.5 Combine like terms: -97.130067435 + -0.5 = -97.630067435 X = -97.630067435 Simplifying X = -97.630067435Solution
The solution to the problem is based on the solutions from the subproblems. X = {96.630067435, -97.630067435}
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