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Simplifying X2 + -14X = -2 Reorder the terms: -14X + X2 = -2 Solving -14X + X2 = -2 Solving for variable 'X'. Reorder the terms: 2 + -14X + X2 = -2 + 2 Combine like terms: -2 + 2 = 0 2 + -14X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -14X + -2 + X2 = 0 + -2 Reorder the terms: 2 + -2 + -14X + X2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -14X + X2 = 0 + -2 -14X + X2 = 0 + -2 Combine like terms: 0 + -2 = -2 -14X + X2 = -2 The X term is -14X. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14X + 49 + X2 = -2 + 49 Reorder the terms: 49 + -14X + X2 = -2 + 49 Combine like terms: -2 + 49 = 47 49 + -14X + X2 = 47 Factor a perfect square on the left side: (X + -7)(X + -7) = 47 Calculate the square root of the right side: 6.8556546 Break this problem into two subproblems by setting (X + -7) equal to 6.8556546 and -6.8556546.Subproblem 1
X + -7 = 6.8556546 Simplifying X + -7 = 6.8556546 Reorder the terms: -7 + X = 6.8556546 Solving -7 + X = 6.8556546 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + X = 6.8556546 + 7 Combine like terms: -7 + 7 = 0 0 + X = 6.8556546 + 7 X = 6.8556546 + 7 Combine like terms: 6.8556546 + 7 = 13.8556546 X = 13.8556546 Simplifying X = 13.8556546Subproblem 2
X + -7 = -6.8556546 Simplifying X + -7 = -6.8556546 Reorder the terms: -7 + X = -6.8556546 Solving -7 + X = -6.8556546 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + X = -6.8556546 + 7 Combine like terms: -7 + 7 = 0 0 + X = -6.8556546 + 7 X = -6.8556546 + 7 Combine like terms: -6.8556546 + 7 = 0.1443454 X = 0.1443454 Simplifying X = 0.1443454Solution
The solution to the problem is based on the solutions from the subproblems. X = {13.8556546, 0.1443454}
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