324=x^2+22x+7

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Solution for 324=x^2+22x+7 equation:


Simplifying
324 = x2 + 22x + 7

Reorder the terms:
324 = 7 + 22x + x2

Solving
324 = 7 + 22x + x2

Solving for variable 'x'.

Combine like terms: 324 + -7 = 317
317 + -22x + -1x2 = 7 + 22x + x2 + -7 + -22x + -1x2

Reorder the terms:
317 + -22x + -1x2 = 7 + -7 + 22x + -22x + x2 + -1x2

Combine like terms: 7 + -7 = 0
317 + -22x + -1x2 = 0 + 22x + -22x + x2 + -1x2
317 + -22x + -1x2 = 22x + -22x + x2 + -1x2

Combine like terms: 22x + -22x = 0
317 + -22x + -1x2 = 0 + x2 + -1x2
317 + -22x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
317 + -22x + -1x2 = 0

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

Divide each side by '-1'.
-317 + 22x + x2 = 0

Move the constant term to the right:

Add '317' to each side of the equation.
-317 + 22x + 317 + x2 = 0 + 317

Reorder the terms:
-317 + 317 + 22x + x2 = 0 + 317

Combine like terms: -317 + 317 = 0
0 + 22x + x2 = 0 + 317
22x + x2 = 0 + 317

Combine like terms: 0 + 317 = 317
22x + x2 = 317

The x term is 22x.  Take half its coefficient (11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
22x + 121 + x2 = 317 + 121

Reorder the terms:
121 + 22x + x2 = 317 + 121

Combine like terms: 317 + 121 = 438
121 + 22x + x2 = 438

Factor a perfect square on the left side:
(x + 11)(x + 11) = 438

Calculate the square root of the right side: 20.928449536

Break this problem into two subproblems by setting 
(x + 11) equal to 20.928449536 and -20.928449536.

Subproblem 1

x + 11 = 20.928449536 Simplifying x + 11 = 20.928449536 Reorder the terms: 11 + x = 20.928449536 Solving 11 + x = 20.928449536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = 20.928449536 + -11 Combine like terms: 11 + -11 = 0 0 + x = 20.928449536 + -11 x = 20.928449536 + -11 Combine like terms: 20.928449536 + -11 = 9.928449536 x = 9.928449536 Simplifying x = 9.928449536

Subproblem 2

x + 11 = -20.928449536 Simplifying x + 11 = -20.928449536 Reorder the terms: 11 + x = -20.928449536 Solving 11 + x = -20.928449536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = -20.928449536 + -11 Combine like terms: 11 + -11 = 0 0 + x = -20.928449536 + -11 x = -20.928449536 + -11 Combine like terms: -20.928449536 + -11 = -31.928449536 x = -31.928449536 Simplifying x = -31.928449536

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.928449536, -31.928449536}

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