x^2-14x=-36

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Solution for x^2-14x=-36 equation:


Simplifying
x2 + -14x = -36

Reorder the terms:
-14x + x2 = -36

Solving
-14x + x2 = -36

Solving for variable 'x'.

Reorder the terms:
36 + -14x + x2 = -36 + 36

Combine like terms: -36 + 36 = 0
36 + -14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-36' to each side of the equation.
36 + -14x + -36 + x2 = 0 + -36

Reorder the terms:
36 + -36 + -14x + x2 = 0 + -36

Combine like terms: 36 + -36 = 0
0 + -14x + x2 = 0 + -36
-14x + x2 = 0 + -36

Combine like terms: 0 + -36 = -36
-14x + x2 = -36

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 = -36 + 49

Reorder the terms:
49 + -14x + x2 = -36 + 49

Combine like terms: -36 + 49 = 13
49 + -14x + x2 = 13

Factor a perfect square on the left side:
(x + -7)(x + -7) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(x + -7) equal to 3.605551275 and -3.605551275.

Subproblem 1

x + -7 = 3.605551275 Simplifying x + -7 = 3.605551275 Reorder the terms: -7 + x = 3.605551275 Solving -7 + x = 3.605551275 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 = 3.605551275 + 7 Combine like terms: -7 + 7 = 0 0 + x = 3.605551275 + 7 x = 3.605551275 + 7 Combine like terms: 3.605551275 + 7 = 10.605551275 x = 10.605551275 Simplifying x = 10.605551275

Subproblem 2

x + -7 = -3.605551275 Simplifying x + -7 = -3.605551275 Reorder the terms: -7 + x = -3.605551275 Solving -7 + x = -3.605551275 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 = -3.605551275 + 7 Combine like terms: -7 + 7 = 0 0 + x = -3.605551275 + 7 x = -3.605551275 + 7 Combine like terms: -3.605551275 + 7 = 3.394448725 x = 3.394448725 Simplifying x = 3.394448725

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.605551275, 3.394448725}

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