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Simplifying x2 + -14x + 4 = 0 Reorder the terms: 4 + -14x + x2 = 0 Solving 4 + -14x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -14x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -14x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -14x + x2 = 0 + -4 -14x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -14x + x2 = -4 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 = -4 + 49 Reorder the terms: 49 + -14x + x2 = -4 + 49 Combine like terms: -4 + 49 = 45 49 + -14x + x2 = 45 Factor a perfect square on the left side: (x + -7)(x + -7) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (x + -7) equal to 6.708203933 and -6.708203933.Subproblem 1
x + -7 = 6.708203933 Simplifying x + -7 = 6.708203933 Reorder the terms: -7 + x = 6.708203933 Solving -7 + x = 6.708203933 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 = 6.708203933 + 7 Combine like terms: -7 + 7 = 0 0 + x = 6.708203933 + 7 x = 6.708203933 + 7 Combine like terms: 6.708203933 + 7 = 13.708203933 x = 13.708203933 Simplifying x = 13.708203933Subproblem 2
x + -7 = -6.708203933 Simplifying x + -7 = -6.708203933 Reorder the terms: -7 + x = -6.708203933 Solving -7 + x = -6.708203933 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 = -6.708203933 + 7 Combine like terms: -7 + 7 = 0 0 + x = -6.708203933 + 7 x = -6.708203933 + 7 Combine like terms: -6.708203933 + 7 = 0.291796067 x = 0.291796067 Simplifying x = 0.291796067Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.708203933, 0.291796067}
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