x^2-40=5x+4

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Solution for x^2-40=5x+4 equation:


Simplifying
x2 + -40 = 5x + 4

Reorder the terms:
-40 + x2 = 5x + 4

Reorder the terms:
-40 + x2 = 4 + 5x

Solving
-40 + x2 = 4 + 5x

Solving for variable 'x'.

Reorder the terms:
-40 + -4 + -5x + x2 = 4 + 5x + -4 + -5x

Combine like terms: -40 + -4 = -44
-44 + -5x + x2 = 4 + 5x + -4 + -5x

Reorder the terms:
-44 + -5x + x2 = 4 + -4 + 5x + -5x

Combine like terms: 4 + -4 = 0
-44 + -5x + x2 = 0 + 5x + -5x
-44 + -5x + x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-44 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '44' to each side of the equation.
-44 + -5x + 44 + x2 = 0 + 44

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

Combine like terms: -44 + 44 = 0
0 + -5x + x2 = 0 + 44
-5x + x2 = 0 + 44

Combine like terms: 0 + 44 = 44
-5x + x2 = 44

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 = 44 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 44 + 6.25

Combine like terms: 44 + 6.25 = 50.25
6.25 + -5x + x2 = 50.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 50.25

Calculate the square root of the right side: 7.088723439

Break this problem into two subproblems by setting 
(x + -2.5) equal to 7.088723439 and -7.088723439.

Subproblem 1

x + -2.5 = 7.088723439 Simplifying x + -2.5 = 7.088723439 Reorder the terms: -2.5 + x = 7.088723439 Solving -2.5 + x = 7.088723439 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 = 7.088723439 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 7.088723439 + 2.5 x = 7.088723439 + 2.5 Combine like terms: 7.088723439 + 2.5 = 9.588723439 x = 9.588723439 Simplifying x = 9.588723439

Subproblem 2

x + -2.5 = -7.088723439 Simplifying x + -2.5 = -7.088723439 Reorder the terms: -2.5 + x = -7.088723439 Solving -2.5 + x = -7.088723439 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 = -7.088723439 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -7.088723439 + 2.5 x = -7.088723439 + 2.5 Combine like terms: -7.088723439 + 2.5 = -4.588723439 x = -4.588723439 Simplifying x = -4.588723439

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.588723439, -4.588723439}

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