x^2-14x=13

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Solution for x^2-14x=13 equation:


Simplifying
x2 + -14x = 13

Reorder the terms:
-14x + x2 = 13

Solving
-14x + x2 = 13

Solving for variable 'x'.

Reorder the terms:
-13 + -14x + x2 = 13 + -13

Combine like terms: 13 + -13 = 0
-13 + -14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + -14x + 13 + x2 = 0 + 13

Reorder the terms:
-13 + 13 + -14x + x2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -14x + x2 = 0 + 13
-14x + x2 = 0 + 13

Combine like terms: 0 + 13 = 13
-14x + x2 = 13

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 = 13 + 49

Reorder the terms:
49 + -14x + x2 = 13 + 49

Combine like terms: 13 + 49 = 62
49 + -14x + x2 = 62

Factor a perfect square on the left side:
(x + -7)(x + -7) = 62

Calculate the square root of the right side: 7.874007874

Break this problem into two subproblems by setting 
(x + -7) equal to 7.874007874 and -7.874007874.

Subproblem 1

x + -7 = 7.874007874 Simplifying x + -7 = 7.874007874 Reorder the terms: -7 + x = 7.874007874 Solving -7 + x = 7.874007874 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 = 7.874007874 + 7 Combine like terms: -7 + 7 = 0 0 + x = 7.874007874 + 7 x = 7.874007874 + 7 Combine like terms: 7.874007874 + 7 = 14.874007874 x = 14.874007874 Simplifying x = 14.874007874

Subproblem 2

x + -7 = -7.874007874 Simplifying x + -7 = -7.874007874 Reorder the terms: -7 + x = -7.874007874 Solving -7 + x = -7.874007874 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 = -7.874007874 + 7 Combine like terms: -7 + 7 = 0 0 + x = -7.874007874 + 7 x = -7.874007874 + 7 Combine like terms: -7.874007874 + 7 = -0.874007874 x = -0.874007874 Simplifying x = -0.874007874

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.874007874, -0.874007874}

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