5x^2+36x-66=0

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Solution for 5x^2+36x-66=0 equation:


Simplifying
5x2 + 36x + -66 = 0

Reorder the terms:
-66 + 36x + 5x2 = 0

Solving
-66 + 36x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
-13.2 + 7.2x + x2 = 0

Move the constant term to the right:

Add '13.2' to each side of the equation.
-13.2 + 7.2x + 13.2 + x2 = 0 + 13.2

Reorder the terms:
-13.2 + 13.2 + 7.2x + x2 = 0 + 13.2

Combine like terms: -13.2 + 13.2 = 0.0
0.0 + 7.2x + x2 = 0 + 13.2
7.2x + x2 = 0 + 13.2

Combine like terms: 0 + 13.2 = 13.2
7.2x + x2 = 13.2

The x term is 7.2x.  Take half its coefficient (3.6).
Square it (12.96) and add it to both sides.

Add '12.96' to each side of the equation.
7.2x + 12.96 + x2 = 13.2 + 12.96

Reorder the terms:
12.96 + 7.2x + x2 = 13.2 + 12.96

Combine like terms: 13.2 + 12.96 = 26.16
12.96 + 7.2x + x2 = 26.16

Factor a perfect square on the left side:
(x + 3.6)(x + 3.6) = 26.16

Calculate the square root of the right side: 5.114684741

Break this problem into two subproblems by setting 
(x + 3.6) equal to 5.114684741 and -5.114684741.

Subproblem 1

x + 3.6 = 5.114684741 Simplifying x + 3.6 = 5.114684741 Reorder the terms: 3.6 + x = 5.114684741 Solving 3.6 + x = 5.114684741 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.6' to each side of the equation. 3.6 + -3.6 + x = 5.114684741 + -3.6 Combine like terms: 3.6 + -3.6 = 0.0 0.0 + x = 5.114684741 + -3.6 x = 5.114684741 + -3.6 Combine like terms: 5.114684741 + -3.6 = 1.514684741 x = 1.514684741 Simplifying x = 1.514684741

Subproblem 2

x + 3.6 = -5.114684741 Simplifying x + 3.6 = -5.114684741 Reorder the terms: 3.6 + x = -5.114684741 Solving 3.6 + x = -5.114684741 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.6' to each side of the equation. 3.6 + -3.6 + x = -5.114684741 + -3.6 Combine like terms: 3.6 + -3.6 = 0.0 0.0 + x = -5.114684741 + -3.6 x = -5.114684741 + -3.6 Combine like terms: -5.114684741 + -3.6 = -8.714684741 x = -8.714684741 Simplifying x = -8.714684741

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.514684741, -8.714684741}

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