7x^2+45x-18=0

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Solution for 7x^2+45x-18=0 equation: 


Simplifying
7x2 + 45x + -18 = 0

Reorder the terms:
-18 + 45x + 7x2 = 0

Solving
-18 + 45x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
-2.571428571 + 6.428571429x + x2 = 0

Move the constant term to the right:

Add '2.571428571' to each side of the equation.
-2.571428571 + 6.428571429x + 2.571428571 + x2 = 0 + 2.571428571

Reorder the terms:
-2.571428571 + 2.571428571 + 6.428571429x + x2 = 0 + 2.571428571

Combine like terms: -2.571428571 + 2.571428571 = 0.000000000
0.000000000 + 6.428571429x + x2 = 0 + 2.571428571
6.428571429x + x2 = 0 + 2.571428571

Combine like terms: 0 + 2.571428571 = 2.571428571
6.428571429x + x2 = 2.571428571

The x term is 6.428571429x.  Take half its coefficient (3.214285715).
Square it (10.33163266) and add it to both sides.

Add '10.33163266' to each side of the equation.
6.428571429x + 10.33163266 + x2 = 2.571428571 + 10.33163266

Reorder the terms:
10.33163266 + 6.428571429x + x2 = 2.571428571 + 10.33163266

Combine like terms: 2.571428571 + 10.33163266 = 12.903061231
10.33163266 + 6.428571429x + x2 = 12.903061231

Factor a perfect square on the left side:
(x + 3.214285715)(x + 3.214285715) = 12.903061231

Calculate the square root of the right side: 3.592083133

Break this problem into two subproblems by setting 
(x + 3.214285715) equal to 3.592083133 and -3.592083133.


Subproblem 1
x + 3.214285715 = 3.592083133

Simplifying
x + 3.214285715 = 3.592083133

Reorder the terms:
3.214285715 + x = 3.592083133

Solving
3.214285715 + x = 3.592083133

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3.214285715' to each side of the equation.
3.214285715 + -3.214285715 + x = 3.592083133 + -3.214285715

Combine like terms: 3.214285715 + -3.214285715 = 0.000000000
0.000000000 + x = 3.592083133 + -3.214285715
x = 3.592083133 + -3.214285715

Combine like terms: 3.592083133 + -3.214285715 = 0.377797418
x = 0.377797418

Simplifying
x = 0.377797418


Subproblem 2
x + 3.214285715 = -3.592083133

Simplifying
x + 3.214285715 = -3.592083133

Reorder the terms:
3.214285715 + x = -3.592083133

Solving
3.214285715 + x = -3.592083133

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3.214285715' to each side of the equation.
3.214285715 + -3.214285715 + x = -3.592083133 + -3.214285715

Combine like terms: 3.214285715 + -3.214285715 = 0.000000000
0.000000000 + x = -3.592083133 + -3.214285715
x = -3.592083133 + -3.214285715

Combine like terms: -3.592083133 + -3.214285715 = -6.806368848
x = -6.806368848

Simplifying
x = -6.806368848


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.377797418, -6.806368848}

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