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Simplifying 0 = x2 + -14x + 3 Reorder the terms: 0 = 3 + -14x + x2 Solving 0 = 3 + -14x + x2 Solving for variable 'x'. Combine like terms: 0 + -3 = -3 -3 + 14x + -1x2 = 3 + -14x + x2 + -3 + 14x + -1x2 Reorder the terms: -3 + 14x + -1x2 = 3 + -3 + -14x + 14x + x2 + -1x2 Combine like terms: 3 + -3 = 0 -3 + 14x + -1x2 = 0 + -14x + 14x + x2 + -1x2 -3 + 14x + -1x2 = -14x + 14x + x2 + -1x2 Combine like terms: -14x + 14x = 0 -3 + 14x + -1x2 = 0 + x2 + -1x2 -3 + 14x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -3 + 14x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 3 + -14x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -14x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -14x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -14x + x2 = 0 + -3 -14x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -14x + x2 = -3 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 = -3 + 49 Reorder the terms: 49 + -14x + x2 = -3 + 49 Combine like terms: -3 + 49 = 46 49 + -14x + x2 = 46 Factor a perfect square on the left side: (x + -7)(x + -7) = 46 Calculate the square root of the right side: 6.782329983 Break this problem into two subproblems by setting (x + -7) equal to 6.782329983 and -6.782329983.Subproblem 1
x + -7 = 6.782329983 Simplifying x + -7 = 6.782329983 Reorder the terms: -7 + x = 6.782329983 Solving -7 + x = 6.782329983 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 = 6.782329983 + 7 Combine like terms: -7 + 7 = 0 0 + x = 6.782329983 + 7 x = 6.782329983 + 7 Combine like terms: 6.782329983 + 7 = 13.782329983 x = 13.782329983 Simplifying x = 13.782329983Subproblem 2
x + -7 = -6.782329983 Simplifying x + -7 = -6.782329983 Reorder the terms: -7 + x = -6.782329983 Solving -7 + x = -6.782329983 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 = -6.782329983 + 7 Combine like terms: -7 + 7 = 0 0 + x = -6.782329983 + 7 x = -6.782329983 + 7 Combine like terms: -6.782329983 + 7 = 0.217670017 x = 0.217670017 Simplifying x = 0.217670017Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.782329983, 0.217670017}
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