5x*x+4x-5=0

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Solution for 5x*x+4x-5=0 equation: 


Simplifying
5x * x + 4x + -5 = 0

Multiply x * x
5x2 + 4x + -5 = 0

Reorder the terms:
-5 + 4x + 5x2 = 0

Solving
-5 + 4x + 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'.
-1 + 0.8x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 0.8x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 0.8x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 0.8x + x2 = 0 + 1
0.8x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
0.8x + x2 = 1

The x term is 0.8x.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8x + 0.16 + x2 = 1 + 0.16

Reorder the terms:
0.16 + 0.8x + x2 = 1 + 0.16

Combine like terms: 1 + 0.16 = 1.16
0.16 + 0.8x + x2 = 1.16

Factor a perfect square on the left side:
(x + 0.4)(x + 0.4) = 1.16

Calculate the square root of the right side: 1.077032961

Break this problem into two subproblems by setting 
(x + 0.4) equal to 1.077032961 and -1.077032961.


Subproblem 1
x + 0.4 = 1.077032961

Simplifying
x + 0.4 = 1.077032961

Reorder the terms:
0.4 + x = 1.077032961

Solving
0.4 + x = 1.077032961

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.4' to each side of the equation.
0.4 + -0.4 + x = 1.077032961 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + x = 1.077032961 + -0.4
x = 1.077032961 + -0.4

Combine like terms: 1.077032961 + -0.4 = 0.677032961
x = 0.677032961

Simplifying
x = 0.677032961


Subproblem 2
x + 0.4 = -1.077032961

Simplifying
x + 0.4 = -1.077032961

Reorder the terms:
0.4 + x = -1.077032961

Solving
0.4 + x = -1.077032961

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.4' to each side of the equation.
0.4 + -0.4 + x = -1.077032961 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + x = -1.077032961 + -0.4
x = -1.077032961 + -0.4

Combine like terms: -1.077032961 + -0.4 = -1.477032961
x = -1.477032961

Simplifying
x = -1.477032961


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.677032961, -1.477032961}

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