-40=-4x^2+47x

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Solution for -40=-4x^2+47x equation: 


Simplifying
-40 = -4x2 + 47x

Reorder the terms:
-40 = 47x + -4x2

Solving
-40 = 47x + -4x2

Solving for variable 'x'.

Reorder the terms:
-40 + -47x + 4x2 = 47x + -47x + -4x2 + 4x2

Combine like terms: 47x + -47x = 0
-40 + -47x + 4x2 = 0 + -4x2 + 4x2
-40 + -47x + 4x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
-40 + -47x + 4x2 = 0

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

Divide each side by '4'.
-10 + -11.75x + x2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -11.75x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + -11.75x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -11.75x + x2 = 0 + 10
-11.75x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
-11.75x + x2 = 10

The x term is -11.75x.  Take half its coefficient (-5.875).
Square it (34.515625) and add it to both sides.

Add '34.515625' to each side of the equation.
-11.75x + 34.515625 + x2 = 10 + 34.515625

Reorder the terms:
34.515625 + -11.75x + x2 = 10 + 34.515625

Combine like terms: 10 + 34.515625 = 44.515625
34.515625 + -11.75x + x2 = 44.515625

Factor a perfect square on the left side:
(x + -5.875)(x + -5.875) = 44.515625

Calculate the square root of the right side: 6.672003073

Break this problem into two subproblems by setting 
(x + -5.875) equal to 6.672003073 and -6.672003073.


Subproblem 1
x + -5.875 = 6.672003073

Simplifying
x + -5.875 = 6.672003073

Reorder the terms:
-5.875 + x = 6.672003073

Solving
-5.875 + x = 6.672003073

Solving for variable 'x'.

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

Add '5.875' to each side of the equation.
-5.875 + 5.875 + x = 6.672003073 + 5.875

Combine like terms: -5.875 + 5.875 = 0.000
0.000 + x = 6.672003073 + 5.875
x = 6.672003073 + 5.875

Combine like terms: 6.672003073 + 5.875 = 12.547003073
x = 12.547003073

Simplifying
x = 12.547003073


Subproblem 2
x + -5.875 = -6.672003073

Simplifying
x + -5.875 = -6.672003073

Reorder the terms:
-5.875 + x = -6.672003073

Solving
-5.875 + x = -6.672003073

Solving for variable 'x'.

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

Add '5.875' to each side of the equation.
-5.875 + 5.875 + x = -6.672003073 + 5.875

Combine like terms: -5.875 + 5.875 = 0.000
0.000 + x = -6.672003073 + 5.875
x = -6.672003073 + 5.875

Combine like terms: -6.672003073 + 5.875 = -0.797003073
x = -0.797003073

Simplifying
x = -0.797003073


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.547003073, -0.797003073}

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