5x^2+6x-1224=0

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Solution for 5x^2+6x-1224=0 equation:


Simplifying
5x2 + 6x + -1224 = 0

Reorder the terms:
-1224 + 6x + 5x2 = 0

Solving
-1224 + 6x + 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'.
-244.8 + 1.2x + x2 = 0

Move the constant term to the right:

Add '244.8' to each side of the equation.
-244.8 + 1.2x + 244.8 + x2 = 0 + 244.8

Reorder the terms:
-244.8 + 244.8 + 1.2x + x2 = 0 + 244.8

Combine like terms: -244.8 + 244.8 = 0.0
0.0 + 1.2x + x2 = 0 + 244.8
1.2x + x2 = 0 + 244.8

Combine like terms: 0 + 244.8 = 244.8
1.2x + x2 = 244.8

The x term is 1.2x.  Take half its coefficient (0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
1.2x + 0.36 + x2 = 244.8 + 0.36

Reorder the terms:
0.36 + 1.2x + x2 = 244.8 + 0.36

Combine like terms: 244.8 + 0.36 = 245.16
0.36 + 1.2x + x2 = 245.16

Factor a perfect square on the left side:
(x + 0.6)(x + 0.6) = 245.16

Calculate the square root of the right side: 15.657586021

Break this problem into two subproblems by setting 
(x + 0.6) equal to 15.657586021 and -15.657586021.

Subproblem 1

x + 0.6 = 15.657586021 Simplifying x + 0.6 = 15.657586021 Reorder the terms: 0.6 + x = 15.657586021 Solving 0.6 + x = 15.657586021 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = 15.657586021 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 15.657586021 + -0.6 x = 15.657586021 + -0.6 Combine like terms: 15.657586021 + -0.6 = 15.057586021 x = 15.057586021 Simplifying x = 15.057586021

Subproblem 2

x + 0.6 = -15.657586021 Simplifying x + 0.6 = -15.657586021 Reorder the terms: 0.6 + x = -15.657586021 Solving 0.6 + x = -15.657586021 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = -15.657586021 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -15.657586021 + -0.6 x = -15.657586021 + -0.6 Combine like terms: -15.657586021 + -0.6 = -16.257586021 x = -16.257586021 Simplifying x = -16.257586021

Solution

The solution to the problem is based on the solutions from the subproblems. x = {15.057586021, -16.257586021}

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