x^2+18x=163

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Solution for x^2+18x=163 equation:


Simplifying
x2 + 18x = 163

Reorder the terms:
18x + x2 = 163

Solving
18x + x2 = 163

Solving for variable 'x'.

Reorder the terms:
-163 + 18x + x2 = 163 + -163

Combine like terms: 163 + -163 = 0
-163 + 18x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '163' to each side of the equation.
-163 + 18x + 163 + x2 = 0 + 163

Reorder the terms:
-163 + 163 + 18x + x2 = 0 + 163

Combine like terms: -163 + 163 = 0
0 + 18x + x2 = 0 + 163
18x + x2 = 0 + 163

Combine like terms: 0 + 163 = 163
18x + x2 = 163

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 = 163 + 81

Reorder the terms:
81 + 18x + x2 = 163 + 81

Combine like terms: 163 + 81 = 244
81 + 18x + x2 = 244

Factor a perfect square on the left side:
(x + 9)(x + 9) = 244

Calculate the square root of the right side: 15.620499352

Break this problem into two subproblems by setting 
(x + 9) equal to 15.620499352 and -15.620499352.

Subproblem 1

x + 9 = 15.620499352 Simplifying x + 9 = 15.620499352 Reorder the terms: 9 + x = 15.620499352 Solving 9 + x = 15.620499352 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 = 15.620499352 + -9 Combine like terms: 9 + -9 = 0 0 + x = 15.620499352 + -9 x = 15.620499352 + -9 Combine like terms: 15.620499352 + -9 = 6.620499352 x = 6.620499352 Simplifying x = 6.620499352

Subproblem 2

x + 9 = -15.620499352 Simplifying x + 9 = -15.620499352 Reorder the terms: 9 + x = -15.620499352 Solving 9 + x = -15.620499352 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 = -15.620499352 + -9 Combine like terms: 9 + -9 = 0 0 + x = -15.620499352 + -9 x = -15.620499352 + -9 Combine like terms: -15.620499352 + -9 = -24.620499352 x = -24.620499352 Simplifying x = -24.620499352

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.620499352, -24.620499352}

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