x^2-14x=-9

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Solution for x^2-14x=-9 equation:


Simplifying
x2 + -14x = -9

Reorder the terms:
-14x + x2 = -9

Solving
-14x + x2 = -9

Solving for variable 'x'.

Reorder the terms:
9 + -14x + x2 = -9 + 9

Combine like terms: -9 + 9 = 0
9 + -14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + -14x + -9 + x2 = 0 + -9

Reorder the terms:
9 + -9 + -14x + x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -14x + x2 = 0 + -9
-14x + x2 = 0 + -9

Combine like terms: 0 + -9 = -9
-14x + x2 = -9

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 = -9 + 49

Reorder the terms:
49 + -14x + x2 = -9 + 49

Combine like terms: -9 + 49 = 40
49 + -14x + x2 = 40

Factor a perfect square on the left side:
(x + -7)(x + -7) = 40

Calculate the square root of the right side: 6.32455532

Break this problem into two subproblems by setting 
(x + -7) equal to 6.32455532 and -6.32455532.

Subproblem 1

x + -7 = 6.32455532 Simplifying x + -7 = 6.32455532 Reorder the terms: -7 + x = 6.32455532 Solving -7 + x = 6.32455532 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 = 6.32455532 + 7 Combine like terms: -7 + 7 = 0 0 + x = 6.32455532 + 7 x = 6.32455532 + 7 Combine like terms: 6.32455532 + 7 = 13.32455532 x = 13.32455532 Simplifying x = 13.32455532

Subproblem 2

x + -7 = -6.32455532 Simplifying x + -7 = -6.32455532 Reorder the terms: -7 + x = -6.32455532 Solving -7 + x = -6.32455532 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 = -6.32455532 + 7 Combine like terms: -7 + 7 = 0 0 + x = -6.32455532 + 7 x = -6.32455532 + 7 Combine like terms: -6.32455532 + 7 = 0.67544468 x = 0.67544468 Simplifying x = 0.67544468

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.32455532, 0.67544468}

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