5x^2+72x+114=0

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Solution for 5x^2+72x+114=0 equation:


Simplifying
5x2 + 72x + 114 = 0

Reorder the terms:
114 + 72x + 5x2 = 0

Solving
114 + 72x + 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'.
22.8 + 14.4x + x2 = 0

Move the constant term to the right:

Add '-22.8' to each side of the equation.
22.8 + 14.4x + -22.8 + x2 = 0 + -22.8

Reorder the terms:
22.8 + -22.8 + 14.4x + x2 = 0 + -22.8

Combine like terms: 22.8 + -22.8 = 0.0
0.0 + 14.4x + x2 = 0 + -22.8
14.4x + x2 = 0 + -22.8

Combine like terms: 0 + -22.8 = -22.8
14.4x + x2 = -22.8

The x term is 14.4x.  Take half its coefficient (7.2).
Square it (51.84) and add it to both sides.

Add '51.84' to each side of the equation.
14.4x + 51.84 + x2 = -22.8 + 51.84

Reorder the terms:
51.84 + 14.4x + x2 = -22.8 + 51.84

Combine like terms: -22.8 + 51.84 = 29.04
51.84 + 14.4x + x2 = 29.04

Factor a perfect square on the left side:
(x + 7.2)(x + 7.2) = 29.04

Calculate the square root of the right side: 5.388877434

Break this problem into two subproblems by setting 
(x + 7.2) equal to 5.388877434 and -5.388877434.

Subproblem 1

x + 7.2 = 5.388877434 Simplifying x + 7.2 = 5.388877434 Reorder the terms: 7.2 + x = 5.388877434 Solving 7.2 + x = 5.388877434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.2' to each side of the equation. 7.2 + -7.2 + x = 5.388877434 + -7.2 Combine like terms: 7.2 + -7.2 = 0.0 0.0 + x = 5.388877434 + -7.2 x = 5.388877434 + -7.2 Combine like terms: 5.388877434 + -7.2 = -1.811122566 x = -1.811122566 Simplifying x = -1.811122566

Subproblem 2

x + 7.2 = -5.388877434 Simplifying x + 7.2 = -5.388877434 Reorder the terms: 7.2 + x = -5.388877434 Solving 7.2 + x = -5.388877434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.2' to each side of the equation. 7.2 + -7.2 + x = -5.388877434 + -7.2 Combine like terms: 7.2 + -7.2 = 0.0 0.0 + x = -5.388877434 + -7.2 x = -5.388877434 + -7.2 Combine like terms: -5.388877434 + -7.2 = -12.588877434 x = -12.588877434 Simplifying x = -12.588877434

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.811122566, -12.588877434}

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