x^2-14x+49=27

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Solution for x^2-14x+49=27 equation:


Simplifying
x2 + -14x + 49 = 27

Reorder the terms:
49 + -14x + x2 = 27

Solving
49 + -14x + x2 = 27

Solving for variable 'x'.

Reorder the terms:
49 + -27 + -14x + x2 = 27 + -27

Combine like terms: 49 + -27 = 22
22 + -14x + x2 = 27 + -27

Combine like terms: 27 + -27 = 0
22 + -14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-22' to each side of the equation.
22 + -14x + -22 + x2 = 0 + -22

Reorder the terms:
22 + -22 + -14x + x2 = 0 + -22

Combine like terms: 22 + -22 = 0
0 + -14x + x2 = 0 + -22
-14x + x2 = 0 + -22

Combine like terms: 0 + -22 = -22
-14x + x2 = -22

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 = -22 + 49

Reorder the terms:
49 + -14x + x2 = -22 + 49

Combine like terms: -22 + 49 = 27
49 + -14x + x2 = 27

Factor a perfect square on the left side:
(x + -7)(x + -7) = 27

Calculate the square root of the right side: 5.196152423

Break this problem into two subproblems by setting 
(x + -7) equal to 5.196152423 and -5.196152423.

Subproblem 1

x + -7 = 5.196152423 Simplifying x + -7 = 5.196152423 Reorder the terms: -7 + x = 5.196152423 Solving -7 + x = 5.196152423 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 = 5.196152423 + 7 Combine like terms: -7 + 7 = 0 0 + x = 5.196152423 + 7 x = 5.196152423 + 7 Combine like terms: 5.196152423 + 7 = 12.196152423 x = 12.196152423 Simplifying x = 12.196152423

Subproblem 2

x + -7 = -5.196152423 Simplifying x + -7 = -5.196152423 Reorder the terms: -7 + x = -5.196152423 Solving -7 + x = -5.196152423 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 = -5.196152423 + 7 Combine like terms: -7 + 7 = 0 0 + x = -5.196152423 + 7 x = -5.196152423 + 7 Combine like terms: -5.196152423 + 7 = 1.803847577 x = 1.803847577 Simplifying x = 1.803847577

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.196152423, 1.803847577}

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