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Simplifying 0 = x2 + -14x + 27 Reorder the terms: 0 = 27 + -14x + x2 Solving 0 = 27 + -14x + x2 Solving for variable 'x'. Combine like terms: 0 + -27 = -27 -27 + 14x + -1x2 = 27 + -14x + x2 + -27 + 14x + -1x2 Reorder the terms: -27 + 14x + -1x2 = 27 + -27 + -14x + 14x + x2 + -1x2 Combine like terms: 27 + -27 = 0 -27 + 14x + -1x2 = 0 + -14x + 14x + x2 + -1x2 -27 + 14x + -1x2 = -14x + 14x + x2 + -1x2 Combine like terms: -14x + 14x = 0 -27 + 14x + -1x2 = 0 + x2 + -1x2 -27 + 14x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -27 + 14x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 27 + -14x + x2 = 0 Move the constant term to the right: Add '-27' to each side of the equation. 27 + -14x + -27 + x2 = 0 + -27 Reorder the terms: 27 + -27 + -14x + x2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -14x + x2 = 0 + -27 -14x + x2 = 0 + -27 Combine like terms: 0 + -27 = -27 -14x + x2 = -27 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 = -27 + 49 Reorder the terms: 49 + -14x + x2 = -27 + 49 Combine like terms: -27 + 49 = 22 49 + -14x + x2 = 22 Factor a perfect square on the left side: (x + -7)(x + -7) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (x + -7) equal to 4.69041576 and -4.69041576.Subproblem 1
x + -7 = 4.69041576 Simplifying x + -7 = 4.69041576 Reorder the terms: -7 + x = 4.69041576 Solving -7 + x = 4.69041576 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 = 4.69041576 + 7 Combine like terms: -7 + 7 = 0 0 + x = 4.69041576 + 7 x = 4.69041576 + 7 Combine like terms: 4.69041576 + 7 = 11.69041576 x = 11.69041576 Simplifying x = 11.69041576Subproblem 2
x + -7 = -4.69041576 Simplifying x + -7 = -4.69041576 Reorder the terms: -7 + x = -4.69041576 Solving -7 + x = -4.69041576 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 = -4.69041576 + 7 Combine like terms: -7 + 7 = 0 0 + x = -4.69041576 + 7 x = -4.69041576 + 7 Combine like terms: -4.69041576 + 7 = 2.30958424 x = 2.30958424 Simplifying x = 2.30958424Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.69041576, 2.30958424}
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