x^2+18x=307

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Solution for x^2+18x=307 equation:


Simplifying
x2 + 18x = 307

Reorder the terms:
18x + x2 = 307

Solving
18x + x2 = 307

Solving for variable 'x'.

Reorder the terms:
-307 + 18x + x2 = 307 + -307

Combine like terms: 307 + -307 = 0
-307 + 18x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '307' to each side of the equation.
-307 + 18x + 307 + x2 = 0 + 307

Reorder the terms:
-307 + 307 + 18x + x2 = 0 + 307

Combine like terms: -307 + 307 = 0
0 + 18x + x2 = 0 + 307
18x + x2 = 0 + 307

Combine like terms: 0 + 307 = 307
18x + x2 = 307

The x term is 18x.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18x + 81 + x2 = 307 + 81

Reorder the terms:
81 + 18x + x2 = 307 + 81

Combine like terms: 307 + 81 = 388
81 + 18x + x2 = 388

Factor a perfect square on the left side:
(x + 9)(x + 9) = 388

Calculate the square root of the right side: 19.697715604

Break this problem into two subproblems by setting 
(x + 9) equal to 19.697715604 and -19.697715604.

Subproblem 1

x + 9 = 19.697715604 Simplifying x + 9 = 19.697715604 Reorder the terms: 9 + x = 19.697715604 Solving 9 + x = 19.697715604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 19.697715604 + -9 Combine like terms: 9 + -9 = 0 0 + x = 19.697715604 + -9 x = 19.697715604 + -9 Combine like terms: 19.697715604 + -9 = 10.697715604 x = 10.697715604 Simplifying x = 10.697715604

Subproblem 2

x + 9 = -19.697715604 Simplifying x + 9 = -19.697715604 Reorder the terms: 9 + x = -19.697715604 Solving 9 + x = -19.697715604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -19.697715604 + -9 Combine like terms: 9 + -9 = 0 0 + x = -19.697715604 + -9 x = -19.697715604 + -9 Combine like terms: -19.697715604 + -9 = -28.697715604 x = -28.697715604 Simplifying x = -28.697715604

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.697715604, -28.697715604}

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