7x(2x+18)=27

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Solution for 7x(2x+18)=27 equation:


Simplifying
7x(2x + 18) = 27

Reorder the terms:
7x(18 + 2x) = 27
(18 * 7x + 2x * 7x) = 27
(126x + 14x2) = 27

Solving
126x + 14x2 = 27

Solving for variable 'x'.

Reorder the terms:
-27 + 126x + 14x2 = 27 + -27

Combine like terms: 27 + -27 = 0
-27 + 126x + 14x2 = 0

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

Divide each side by '14'.
-1.928571429 + 9x + x2 = 0

Move the constant term to the right:

Add '1.928571429' to each side of the equation.
-1.928571429 + 9x + 1.928571429 + x2 = 0 + 1.928571429

Reorder the terms:
-1.928571429 + 1.928571429 + 9x + x2 = 0 + 1.928571429

Combine like terms: -1.928571429 + 1.928571429 = 0.000000000
0.000000000 + 9x + x2 = 0 + 1.928571429
9x + x2 = 0 + 1.928571429

Combine like terms: 0 + 1.928571429 = 1.928571429
9x + x2 = 1.928571429

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = 1.928571429 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 1.928571429 + 20.25

Combine like terms: 1.928571429 + 20.25 = 22.178571429
20.25 + 9x + x2 = 22.178571429

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 22.178571429

Calculate the square root of the right side: 4.709413066

Break this problem into two subproblems by setting 
(x + 4.5) equal to 4.709413066 and -4.709413066.

Subproblem 1

x + 4.5 = 4.709413066 Simplifying x + 4.5 = 4.709413066 Reorder the terms: 4.5 + x = 4.709413066 Solving 4.5 + x = 4.709413066 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 4.709413066 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 4.709413066 + -4.5 x = 4.709413066 + -4.5 Combine like terms: 4.709413066 + -4.5 = 0.209413066 x = 0.209413066 Simplifying x = 0.209413066

Subproblem 2

x + 4.5 = -4.709413066 Simplifying x + 4.5 = -4.709413066 Reorder the terms: 4.5 + x = -4.709413066 Solving 4.5 + x = -4.709413066 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -4.709413066 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -4.709413066 + -4.5 x = -4.709413066 + -4.5 Combine like terms: -4.709413066 + -4.5 = -9.209413066 x = -9.209413066 Simplifying x = -9.209413066

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.209413066, -9.209413066}

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