2x^2+31x-4.7=0

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Solution for 2x^2+31x-4.7=0 equation: 


Simplifying
2x2 + 31x + -4.7 = 0

Reorder the terms:
-4.7 + 31x + 2x2 = 0

Solving
-4.7 + 31x + 2x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-2.35 + 15.5x + x2 = 0

Move the constant term to the right:

Add '2.35' to each side of the equation.
-2.35 + 15.5x + 2.35 + x2 = 0 + 2.35

Reorder the terms:
-2.35 + 2.35 + 15.5x + x2 = 0 + 2.35

Combine like terms: -2.35 + 2.35 = 0.00
0.00 + 15.5x + x2 = 0 + 2.35
15.5x + x2 = 0 + 2.35

Combine like terms: 0 + 2.35 = 2.35
15.5x + x2 = 2.35

The x term is 15.5x.  Take half its coefficient (7.75).
Square it (60.0625) and add it to both sides.

Add '60.0625' to each side of the equation.
15.5x + 60.0625 + x2 = 2.35 + 60.0625

Reorder the terms:
60.0625 + 15.5x + x2 = 2.35 + 60.0625

Combine like terms: 2.35 + 60.0625 = 62.4125
60.0625 + 15.5x + x2 = 62.4125

Factor a perfect square on the left side:
(x + 7.75)(x + 7.75) = 62.4125

Calculate the square root of the right side: 7.900158226

Break this problem into two subproblems by setting 
(x + 7.75) equal to 7.900158226 and -7.900158226.


Subproblem 1
x + 7.75 = 7.900158226

Simplifying
x + 7.75 = 7.900158226

Reorder the terms:
7.75 + x = 7.900158226

Solving
7.75 + x = 7.900158226

Solving for variable 'x'.

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

Add '-7.75' to each side of the equation.
7.75 + -7.75 + x = 7.900158226 + -7.75

Combine like terms: 7.75 + -7.75 = 0.00
0.00 + x = 7.900158226 + -7.75
x = 7.900158226 + -7.75

Combine like terms: 7.900158226 + -7.75 = 0.150158226
x = 0.150158226

Simplifying
x = 0.150158226


Subproblem 2
x + 7.75 = -7.900158226

Simplifying
x + 7.75 = -7.900158226

Reorder the terms:
7.75 + x = -7.900158226

Solving
7.75 + x = -7.900158226

Solving for variable 'x'.

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

Add '-7.75' to each side of the equation.
7.75 + -7.75 + x = -7.900158226 + -7.75

Combine like terms: 7.75 + -7.75 = 0.00
0.00 + x = -7.900158226 + -7.75
x = -7.900158226 + -7.75

Combine like terms: -7.900158226 + -7.75 = -15.650158226
x = -15.650158226

Simplifying
x = -15.650158226


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.150158226, -15.650158226}

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