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Simplifying x2 + -14x = 17 Reorder the terms: -14x + x2 = 17 Solving -14x + x2 = 17 Solving for variable 'x'. Reorder the terms: -17 + -14x + x2 = 17 + -17 Combine like terms: 17 + -17 = 0 -17 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + -14x + 17 + x2 = 0 + 17 Reorder the terms: -17 + 17 + -14x + x2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -14x + x2 = 0 + 17 -14x + x2 = 0 + 17 Combine like terms: 0 + 17 = 17 -14x + x2 = 17 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 = 17 + 49 Reorder the terms: 49 + -14x + x2 = 17 + 49 Combine like terms: 17 + 49 = 66 49 + -14x + x2 = 66 Factor a perfect square on the left side: (x + -7)(x + -7) = 66 Calculate the square root of the right side: 8.124038405 Break this problem into two subproblems by setting (x + -7) equal to 8.124038405 and -8.124038405.Subproblem 1
x + -7 = 8.124038405 Simplifying x + -7 = 8.124038405 Reorder the terms: -7 + x = 8.124038405 Solving -7 + x = 8.124038405 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 = 8.124038405 + 7 Combine like terms: -7 + 7 = 0 0 + x = 8.124038405 + 7 x = 8.124038405 + 7 Combine like terms: 8.124038405 + 7 = 15.124038405 x = 15.124038405 Simplifying x = 15.124038405Subproblem 2
x + -7 = -8.124038405 Simplifying x + -7 = -8.124038405 Reorder the terms: -7 + x = -8.124038405 Solving -7 + x = -8.124038405 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 = -8.124038405 + 7 Combine like terms: -7 + 7 = 0 0 + x = -8.124038405 + 7 x = -8.124038405 + 7 Combine like terms: -8.124038405 + 7 = -1.124038405 x = -1.124038405 Simplifying x = -1.124038405Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.124038405, -1.124038405}
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