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Simplifying x2 + -14x = -31 Reorder the terms: -14x + x2 = -31 Solving -14x + x2 = -31 Solving for variable 'x'. Reorder the terms: 31 + -14x + x2 = -31 + 31 Combine like terms: -31 + 31 = 0 31 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-31' to each side of the equation. 31 + -14x + -31 + x2 = 0 + -31 Reorder the terms: 31 + -31 + -14x + x2 = 0 + -31 Combine like terms: 31 + -31 = 0 0 + -14x + x2 = 0 + -31 -14x + x2 = 0 + -31 Combine like terms: 0 + -31 = -31 -14x + x2 = -31 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 = -31 + 49 Reorder the terms: 49 + -14x + x2 = -31 + 49 Combine like terms: -31 + 49 = 18 49 + -14x + x2 = 18 Factor a perfect square on the left side: (x + -7)(x + -7) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (x + -7) equal to 4.242640687 and -4.242640687.Subproblem 1
x + -7 = 4.242640687 Simplifying x + -7 = 4.242640687 Reorder the terms: -7 + x = 4.242640687 Solving -7 + x = 4.242640687 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 = 4.242640687 + 7 Combine like terms: -7 + 7 = 0 0 + x = 4.242640687 + 7 x = 4.242640687 + 7 Combine like terms: 4.242640687 + 7 = 11.242640687 x = 11.242640687 Simplifying x = 11.242640687Subproblem 2
x + -7 = -4.242640687 Simplifying x + -7 = -4.242640687 Reorder the terms: -7 + x = -4.242640687 Solving -7 + x = -4.242640687 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 = -4.242640687 + 7 Combine like terms: -7 + 7 = 0 0 + x = -4.242640687 + 7 x = -4.242640687 + 7 Combine like terms: -4.242640687 + 7 = 2.757359313 x = 2.757359313 Simplifying x = 2.757359313Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.242640687, 2.757359313}
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