x^2-14x=-38

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Solution for x^2-14x=-38 equation:


Simplifying
x2 + -14x = -38

Reorder the terms:
-14x + x2 = -38

Solving
-14x + x2 = -38

Solving for variable 'x'.

Reorder the terms:
38 + -14x + x2 = -38 + 38

Combine like terms: -38 + 38 = 0
38 + -14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-38' to each side of the equation.
38 + -14x + -38 + x2 = 0 + -38

Reorder the terms:
38 + -38 + -14x + x2 = 0 + -38

Combine like terms: 38 + -38 = 0
0 + -14x + x2 = 0 + -38
-14x + x2 = 0 + -38

Combine like terms: 0 + -38 = -38
-14x + x2 = -38

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 = -38 + 49

Reorder the terms:
49 + -14x + x2 = -38 + 49

Combine like terms: -38 + 49 = 11
49 + -14x + x2 = 11

Factor a perfect square on the left side:
(x + -7)(x + -7) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(x + -7) equal to 3.31662479 and -3.31662479.

Subproblem 1

x + -7 = 3.31662479 Simplifying x + -7 = 3.31662479 Reorder the terms: -7 + x = 3.31662479 Solving -7 + x = 3.31662479 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 = 3.31662479 + 7 Combine like terms: -7 + 7 = 0 0 + x = 3.31662479 + 7 x = 3.31662479 + 7 Combine like terms: 3.31662479 + 7 = 10.31662479 x = 10.31662479 Simplifying x = 10.31662479

Subproblem 2

x + -7 = -3.31662479 Simplifying x + -7 = -3.31662479 Reorder the terms: -7 + x = -3.31662479 Solving -7 + x = -3.31662479 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 = -3.31662479 + 7 Combine like terms: -7 + 7 = 0 0 + x = -3.31662479 + 7 x = -3.31662479 + 7 Combine like terms: -3.31662479 + 7 = 3.68337521 x = 3.68337521 Simplifying x = 3.68337521

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.31662479, 3.68337521}

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