x^2-14x+3=

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Solution for x^2-14x+3= equation:


Simplifying
x2 + -14x + 3 = 0

Reorder the terms:
3 + -14x + x2 = 0

Solving
3 + -14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

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 = 13.782329983

Subproblem 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 = 0.217670017

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.782329983, 0.217670017}

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