600=x(x+40)

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Solution for 600=x(x+40) equation:


Simplifying
600 = x(x + 40)

Reorder the terms:
600 = x(40 + x)
600 = (40 * x + x * x)
600 = (40x + x2)

Solving
600 = 40x + x2

Solving for variable 'x'.

Reorder the terms:
600 + -40x + -1x2 = 40x + -40x + x2 + -1x2

Combine like terms: 40x + -40x = 0
600 + -40x + -1x2 = 0 + x2 + -1x2
600 + -40x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
600 + -40x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-600 + 40x + x2 = 0

Move the constant term to the right:

Add '600' to each side of the equation.
-600 + 40x + 600 + x2 = 0 + 600

Reorder the terms:
-600 + 600 + 40x + x2 = 0 + 600

Combine like terms: -600 + 600 = 0
0 + 40x + x2 = 0 + 600
40x + x2 = 0 + 600

Combine like terms: 0 + 600 = 600
40x + x2 = 600

The x term is 40x.  Take half its coefficient (20).
Square it (400) and add it to both sides.

Add '400' to each side of the equation.
40x + 400 + x2 = 600 + 400

Reorder the terms:
400 + 40x + x2 = 600 + 400

Combine like terms: 600 + 400 = 1000
400 + 40x + x2 = 1000

Factor a perfect square on the left side:
(x + 20)(x + 20) = 1000

Calculate the square root of the right side: 31.622776602

Break this problem into two subproblems by setting 
(x + 20) equal to 31.622776602 and -31.622776602.

Subproblem 1

x + 20 = 31.622776602 Simplifying x + 20 = 31.622776602 Reorder the terms: 20 + x = 31.622776602 Solving 20 + x = 31.622776602 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = 31.622776602 + -20 Combine like terms: 20 + -20 = 0 0 + x = 31.622776602 + -20 x = 31.622776602 + -20 Combine like terms: 31.622776602 + -20 = 11.622776602 x = 11.622776602 Simplifying x = 11.622776602

Subproblem 2

x + 20 = -31.622776602 Simplifying x + 20 = -31.622776602 Reorder the terms: 20 + x = -31.622776602 Solving 20 + x = -31.622776602 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = -31.622776602 + -20 Combine like terms: 20 + -20 = 0 0 + x = -31.622776602 + -20 x = -31.622776602 + -20 Combine like terms: -31.622776602 + -20 = -51.622776602 x = -51.622776602 Simplifying x = -51.622776602

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.622776602, -51.622776602}

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