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Simplifying X2 + 7 = 7X + 3 Reorder the terms: 7 + X2 = 7X + 3 Reorder the terms: 7 + X2 = 3 + 7X Solving 7 + X2 = 3 + 7X Solving for variable 'X'. Reorder the terms: 7 + -3 + -7X + X2 = 3 + 7X + -3 + -7X Combine like terms: 7 + -3 = 4 4 + -7X + X2 = 3 + 7X + -3 + -7X Reorder the terms: 4 + -7X + X2 = 3 + -3 + 7X + -7X Combine like terms: 3 + -3 = 0 4 + -7X + X2 = 0 + 7X + -7X 4 + -7X + X2 = 7X + -7X Combine like terms: 7X + -7X = 0 4 + -7X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -7X + -4 + X2 = 0 + -4 Reorder the terms: 4 + -4 + -7X + X2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7X + X2 = 0 + -4 -7X + X2 = 0 + -4 Combine like terms: 0 + -4 = -4 -7X + X2 = -4 The X term is -7X. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7X + 12.25 + X2 = -4 + 12.25 Reorder the terms: 12.25 + -7X + X2 = -4 + 12.25 Combine like terms: -4 + 12.25 = 8.25 12.25 + -7X + X2 = 8.25 Factor a perfect square on the left side: (X + -3.5)(X + -3.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (X + -3.5) equal to 2.872281323 and -2.872281323.Subproblem 1
X + -3.5 = 2.872281323 Simplifying X + -3.5 = 2.872281323 Reorder the terms: -3.5 + X = 2.872281323 Solving -3.5 + X = 2.872281323 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + X = 2.872281323 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + X = 2.872281323 + 3.5 X = 2.872281323 + 3.5 Combine like terms: 2.872281323 + 3.5 = 6.372281323 X = 6.372281323 Simplifying X = 6.372281323Subproblem 2
X + -3.5 = -2.872281323 Simplifying X + -3.5 = -2.872281323 Reorder the terms: -3.5 + X = -2.872281323 Solving -3.5 + X = -2.872281323 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + X = -2.872281323 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + X = -2.872281323 + 3.5 X = -2.872281323 + 3.5 Combine like terms: -2.872281323 + 3.5 = 0.627718677 X = 0.627718677 Simplifying X = 0.627718677Solution
The solution to the problem is based on the solutions from the subproblems. X = {6.372281323, 0.627718677}
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