25(2)+81=x^2-14x+49

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Solution for 25(2)+81=x^2-14x+49 equation:


Simplifying
25(2) + 81 = x2 + -14x + 49

Multiply 25 * 2
50 + 81 = x2 + -14x + 49

Combine like terms: 50 + 81 = 131
131 = x2 + -14x + 49

Reorder the terms:
131 = 49 + -14x + x2

Solving
131 = 49 + -14x + x2

Solving for variable 'x'.

Combine like terms: 131 + -49 = 82
82 + 14x + -1x2 = 49 + -14x + x2 + -49 + 14x + -1x2

Reorder the terms:
82 + 14x + -1x2 = 49 + -49 + -14x + 14x + x2 + -1x2

Combine like terms: 49 + -49 = 0
82 + 14x + -1x2 = 0 + -14x + 14x + x2 + -1x2
82 + 14x + -1x2 = -14x + 14x + x2 + -1x2

Combine like terms: -14x + 14x = 0
82 + 14x + -1x2 = 0 + x2 + -1x2
82 + 14x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
82 + 14x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-82 + -14x + x2 = 0

Move the constant term to the right:

Add '82' to each side of the equation.
-82 + -14x + 82 + x2 = 0 + 82

Reorder the terms:
-82 + 82 + -14x + x2 = 0 + 82

Combine like terms: -82 + 82 = 0
0 + -14x + x2 = 0 + 82
-14x + x2 = 0 + 82

Combine like terms: 0 + 82 = 82
-14x + x2 = 82

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 = 82 + 49

Reorder the terms:
49 + -14x + x2 = 82 + 49

Combine like terms: 82 + 49 = 131
49 + -14x + x2 = 131

Factor a perfect square on the left side:
(x + -7)(x + -7) = 131

Calculate the square root of the right side: 11.445523142

Break this problem into two subproblems by setting 
(x + -7) equal to 11.445523142 and -11.445523142.

Subproblem 1

x + -7 = 11.445523142 Simplifying x + -7 = 11.445523142 Reorder the terms: -7 + x = 11.445523142 Solving -7 + x = 11.445523142 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 = 11.445523142 + 7 Combine like terms: -7 + 7 = 0 0 + x = 11.445523142 + 7 x = 11.445523142 + 7 Combine like terms: 11.445523142 + 7 = 18.445523142 x = 18.445523142 Simplifying x = 18.445523142

Subproblem 2

x + -7 = -11.445523142 Simplifying x + -7 = -11.445523142 Reorder the terms: -7 + x = -11.445523142 Solving -7 + x = -11.445523142 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 = -11.445523142 + 7 Combine like terms: -7 + 7 = 0 0 + x = -11.445523142 + 7 x = -11.445523142 + 7 Combine like terms: -11.445523142 + 7 = -4.445523142 x = -4.445523142 Simplifying x = -4.445523142

Solution

The solution to the problem is based on the solutions from the subproblems. x = {18.445523142, -4.445523142}

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