5x^2+25x-44=0

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Solution for 5x^2+25x-44=0 equation:


Simplifying
5x2 + 25x + -44 = 0

Reorder the terms:
-44 + 25x + 5x2 = 0

Solving
-44 + 25x + 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'.
-8.8 + 5x + x2 = 0

Move the constant term to the right:

Add '8.8' to each side of the equation.
-8.8 + 5x + 8.8 + x2 = 0 + 8.8

Reorder the terms:
-8.8 + 8.8 + 5x + x2 = 0 + 8.8

Combine like terms: -8.8 + 8.8 = 0.0
0.0 + 5x + x2 = 0 + 8.8
5x + x2 = 0 + 8.8

Combine like terms: 0 + 8.8 = 8.8
5x + x2 = 8.8

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 8.8 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 8.8 + 6.25

Combine like terms: 8.8 + 6.25 = 15.05
6.25 + 5x + x2 = 15.05

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 15.05

Calculate the square root of the right side: 3.879432948

Break this problem into two subproblems by setting 
(x + 2.5) equal to 3.879432948 and -3.879432948.

Subproblem 1

x + 2.5 = 3.879432948 Simplifying x + 2.5 = 3.879432948 Reorder the terms: 2.5 + x = 3.879432948 Solving 2.5 + x = 3.879432948 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 3.879432948 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 3.879432948 + -2.5 x = 3.879432948 + -2.5 Combine like terms: 3.879432948 + -2.5 = 1.379432948 x = 1.379432948 Simplifying x = 1.379432948

Subproblem 2

x + 2.5 = -3.879432948 Simplifying x + 2.5 = -3.879432948 Reorder the terms: 2.5 + x = -3.879432948 Solving 2.5 + x = -3.879432948 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -3.879432948 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -3.879432948 + -2.5 x = -3.879432948 + -2.5 Combine like terms: -3.879432948 + -2.5 = -6.379432948 x = -6.379432948 Simplifying x = -6.379432948

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.379432948, -6.379432948}

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