5x^2+12x-36=0

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Solution for 5x^2+12x-36=0 equation:


Simplifying
5x2 + 12x + -36 = 0

Reorder the terms:
-36 + 12x + 5x2 = 0

Solving
-36 + 12x + 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'.
-7.2 + 2.4x + x2 = 0

Move the constant term to the right:

Add '7.2' to each side of the equation.
-7.2 + 2.4x + 7.2 + x2 = 0 + 7.2

Reorder the terms:
-7.2 + 7.2 + 2.4x + x2 = 0 + 7.2

Combine like terms: -7.2 + 7.2 = 0.0
0.0 + 2.4x + x2 = 0 + 7.2
2.4x + x2 = 0 + 7.2

Combine like terms: 0 + 7.2 = 7.2
2.4x + x2 = 7.2

The x term is 2.4x.  Take half its coefficient (1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
2.4x + 1.44 + x2 = 7.2 + 1.44

Reorder the terms:
1.44 + 2.4x + x2 = 7.2 + 1.44

Combine like terms: 7.2 + 1.44 = 8.64
1.44 + 2.4x + x2 = 8.64

Factor a perfect square on the left side:
(x + 1.2)(x + 1.2) = 8.64

Calculate the square root of the right side: 2.939387691

Break this problem into two subproblems by setting 
(x + 1.2) equal to 2.939387691 and -2.939387691.

Subproblem 1

x + 1.2 = 2.939387691 Simplifying x + 1.2 = 2.939387691 Reorder the terms: 1.2 + x = 2.939387691 Solving 1.2 + x = 2.939387691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = 2.939387691 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = 2.939387691 + -1.2 x = 2.939387691 + -1.2 Combine like terms: 2.939387691 + -1.2 = 1.739387691 x = 1.739387691 Simplifying x = 1.739387691

Subproblem 2

x + 1.2 = -2.939387691 Simplifying x + 1.2 = -2.939387691 Reorder the terms: 1.2 + x = -2.939387691 Solving 1.2 + x = -2.939387691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = -2.939387691 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = -2.939387691 + -1.2 x = -2.939387691 + -1.2 Combine like terms: -2.939387691 + -1.2 = -4.139387691 x = -4.139387691 Simplifying x = -4.139387691

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.739387691, -4.139387691}

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