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Simplifying X + 7 = X2 + -4 Reorder the terms: 7 + X = X2 + -4 Reorder the terms: 7 + X = -4 + X2 Solving 7 + X = -4 + X2 Solving for variable 'X'. Reorder the terms: 7 + 4 + X + -1X2 = -4 + X2 + 4 + -1X2 Combine like terms: 7 + 4 = 11 11 + X + -1X2 = -4 + X2 + 4 + -1X2 Reorder the terms: 11 + X + -1X2 = -4 + 4 + X2 + -1X2 Combine like terms: -4 + 4 = 0 11 + X + -1X2 = 0 + X2 + -1X2 11 + X + -1X2 = X2 + -1X2 Combine like terms: X2 + -1X2 = 0 11 + X + -1X2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -11 + -1X + X2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + -1X + 11 + X2 = 0 + 11 Reorder the terms: -11 + 11 + -1X + X2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -1X + X2 = 0 + 11 -1X + X2 = 0 + 11 Combine like terms: 0 + 11 = 11 -1X + X2 = 11 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. -1X + 0.25 + X2 = 11 + 0.25 Reorder the terms: 0.25 + -1X + X2 = 11 + 0.25 Combine like terms: 11 + 0.25 = 11.25 0.25 + -1X + X2 = 11.25 Factor a perfect square on the left side: (X + 0.5)(X + 0.5) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (X + 0.5) equal to 3.354101966 and -3.354101966.Subproblem 1
X + 0.5 = 3.354101966 Simplifying X + 0.5 = 3.354101966 Reorder the terms: 0.5 + X = 3.354101966 Solving 0.5 + X = 3.354101966 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 = 3.354101966 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = 3.354101966 + -0.5 X = 3.354101966 + -0.5 Combine like terms: 3.354101966 + -0.5 = 2.854101966 X = 2.854101966 Simplifying X = 2.854101966Subproblem 2
X + 0.5 = -3.354101966 Simplifying X + 0.5 = -3.354101966 Reorder the terms: 0.5 + X = -3.354101966 Solving 0.5 + X = -3.354101966 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 = -3.354101966 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = -3.354101966 + -0.5 X = -3.354101966 + -0.5 Combine like terms: -3.354101966 + -0.5 = -3.854101966 X = -3.854101966 Simplifying X = -3.854101966Solution
The solution to the problem is based on the solutions from the subproblems. X = {2.854101966, -3.854101966}
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