x^2-14x+4=0

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Solution for x^2-14x+4=0 equation:


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 = 13.708203933

Subproblem 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 = 0.291796067

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.708203933, 0.291796067}

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