5x^2+40x+79=0

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Solution for 5x^2+40x+79=0 equation:


Simplifying
5x2 + 40x + 79 = 0

Reorder the terms:
79 + 40x + 5x2 = 0

Solving
79 + 40x + 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'.
15.8 + 8x + x2 = 0

Move the constant term to the right:

Add '-15.8' to each side of the equation.
15.8 + 8x + -15.8 + x2 = 0 + -15.8

Reorder the terms:
15.8 + -15.8 + 8x + x2 = 0 + -15.8

Combine like terms: 15.8 + -15.8 = 0.0
0.0 + 8x + x2 = 0 + -15.8
8x + x2 = 0 + -15.8

Combine like terms: 0 + -15.8 = -15.8
8x + x2 = -15.8

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = -15.8 + 16

Reorder the terms:
16 + 8x + x2 = -15.8 + 16

Combine like terms: -15.8 + 16 = 0.2
16 + 8x + x2 = 0.2

Factor a perfect square on the left side:
(x + 4)(x + 4) = 0.2

Calculate the square root of the right side: 0.447213596

Break this problem into two subproblems by setting 
(x + 4) equal to 0.447213596 and -0.447213596.

Subproblem 1

x + 4 = 0.447213596 Simplifying x + 4 = 0.447213596 Reorder the terms: 4 + x = 0.447213596 Solving 4 + x = 0.447213596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0.447213596 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0.447213596 + -4 x = 0.447213596 + -4 Combine like terms: 0.447213596 + -4 = -3.552786404 x = -3.552786404 Simplifying x = -3.552786404

Subproblem 2

x + 4 = -0.447213596 Simplifying x + 4 = -0.447213596 Reorder the terms: 4 + x = -0.447213596 Solving 4 + x = -0.447213596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -0.447213596 + -4 Combine like terms: 4 + -4 = 0 0 + x = -0.447213596 + -4 x = -0.447213596 + -4 Combine like terms: -0.447213596 + -4 = -4.447213596 x = -4.447213596 Simplifying x = -4.447213596

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-3.552786404, -4.447213596}

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