5X^2+12X-58=0

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Solution for 5X^2+12X-58=0 equation:


Simplifying
5X2 + 12X + -58 = 0

Reorder the terms:
-58 + 12X + 5X2 = 0

Solving
-58 + 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'.
-11.6 + 2.4X + X2 = 0

Move the constant term to the right:

Add '11.6' to each side of the equation.
-11.6 + 2.4X + 11.6 + X2 = 0 + 11.6

Reorder the terms:
-11.6 + 11.6 + 2.4X + X2 = 0 + 11.6

Combine like terms: -11.6 + 11.6 = 0.0
0.0 + 2.4X + X2 = 0 + 11.6
2.4X + X2 = 0 + 11.6

Combine like terms: 0 + 11.6 = 11.6
2.4X + X2 = 11.6

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 = 11.6 + 1.44

Reorder the terms:
1.44 + 2.4X + X2 = 11.6 + 1.44

Combine like terms: 11.6 + 1.44 = 13.04
1.44 + 2.4X + X2 = 13.04

Factor a perfect square on the left side:
(X + 1.2)(X + 1.2) = 13.04

Calculate the square root of the right side: 3.611094017

Break this problem into two subproblems by setting 
(X + 1.2) equal to 3.611094017 and -3.611094017.

Subproblem 1

X + 1.2 = 3.611094017 Simplifying X + 1.2 = 3.611094017 Reorder the terms: 1.2 + X = 3.611094017 Solving 1.2 + X = 3.611094017 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 = 3.611094017 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + X = 3.611094017 + -1.2 X = 3.611094017 + -1.2 Combine like terms: 3.611094017 + -1.2 = 2.411094017 X = 2.411094017 Simplifying X = 2.411094017

Subproblem 2

X + 1.2 = -3.611094017 Simplifying X + 1.2 = -3.611094017 Reorder the terms: 1.2 + X = -3.611094017 Solving 1.2 + X = -3.611094017 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 = -3.611094017 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + X = -3.611094017 + -1.2 X = -3.611094017 + -1.2 Combine like terms: -3.611094017 + -1.2 = -4.811094017 X = -4.811094017 Simplifying X = -4.811094017

Solution

The solution to the problem is based on the solutions from the subproblems. X = {2.411094017, -4.811094017}

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