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Simplifying 0 = x2 + -14x + 2 Reorder the terms: 0 = 2 + -14x + x2 Solving 0 = 2 + -14x + x2 Solving for variable 'x'. Combine like terms: 0 + -2 = -2 -2 + 14x + -1x2 = 2 + -14x + x2 + -2 + 14x + -1x2 Reorder the terms: -2 + 14x + -1x2 = 2 + -2 + -14x + 14x + x2 + -1x2 Combine like terms: 2 + -2 = 0 -2 + 14x + -1x2 = 0 + -14x + 14x + x2 + -1x2 -2 + 14x + -1x2 = -14x + 14x + x2 + -1x2 Combine like terms: -14x + 14x = 0 -2 + 14x + -1x2 = 0 + x2 + -1x2 -2 + 14x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -2 + 14x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2 + -14x + x2 = 0 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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