5x^2+72x+34=0

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Solution for 5x^2+72x+34=0 equation:


Simplifying
5x2 + 72x + 34 = 0

Reorder the terms:
34 + 72x + 5x2 = 0

Solving
34 + 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'.
6.8 + 14.4x + x2 = 0

Move the constant term to the right:

Add '-6.8' to each side of the equation.
6.8 + 14.4x + -6.8 + x2 = 0 + -6.8

Reorder the terms:
6.8 + -6.8 + 14.4x + x2 = 0 + -6.8

Combine like terms: 6.8 + -6.8 = 0.0
0.0 + 14.4x + x2 = 0 + -6.8
14.4x + x2 = 0 + -6.8

Combine like terms: 0 + -6.8 = -6.8
14.4x + x2 = -6.8

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 = -6.8 + 51.84

Reorder the terms:
51.84 + 14.4x + x2 = -6.8 + 51.84

Combine like terms: -6.8 + 51.84 = 45.04
51.84 + 14.4x + x2 = 45.04

Factor a perfect square on the left side:
(x + 7.2)(x + 7.2) = 45.04

Calculate the square root of the right side: 6.711184694

Break this problem into two subproblems by setting 
(x + 7.2) equal to 6.711184694 and -6.711184694.

Subproblem 1

x + 7.2 = 6.711184694 Simplifying x + 7.2 = 6.711184694 Reorder the terms: 7.2 + x = 6.711184694 Solving 7.2 + x = 6.711184694 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 = 6.711184694 + -7.2 Combine like terms: 7.2 + -7.2 = 0.0 0.0 + x = 6.711184694 + -7.2 x = 6.711184694 + -7.2 Combine like terms: 6.711184694 + -7.2 = -0.488815306 x = -0.488815306 Simplifying x = -0.488815306

Subproblem 2

x + 7.2 = -6.711184694 Simplifying x + 7.2 = -6.711184694 Reorder the terms: 7.2 + x = -6.711184694 Solving 7.2 + x = -6.711184694 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 = -6.711184694 + -7.2 Combine like terms: 7.2 + -7.2 = 0.0 0.0 + x = -6.711184694 + -7.2 x = -6.711184694 + -7.2 Combine like terms: -6.711184694 + -7.2 = -13.911184694 x = -13.911184694 Simplifying x = -13.911184694

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.488815306, -13.911184694}

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