48=x(x+6)

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Solution for 48=x(x+6) equation:


Simplifying
48 = x(x + 6)

Reorder the terms:
48 = x(6 + x)
48 = (6 * x + x * x)
48 = (6x + x2)

Solving
48 = 6x + x2

Solving for variable 'x'.

Reorder the terms:
48 + -6x + -1x2 = 6x + -6x + x2 + -1x2

Combine like terms: 6x + -6x = 0
48 + -6x + -1x2 = 0 + x2 + -1x2
48 + -6x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
48 + -6x + -1x2 = 0

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

Divide each side by '-1'.
-48 + 6x + x2 = 0

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + 6x + 48 + x2 = 0 + 48

Reorder the terms:
-48 + 48 + 6x + x2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + 6x + x2 = 0 + 48
6x + x2 = 0 + 48

Combine like terms: 0 + 48 = 48
6x + x2 = 48

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 48 + 9

Reorder the terms:
9 + 6x + x2 = 48 + 9

Combine like terms: 48 + 9 = 57
9 + 6x + x2 = 57

Factor a perfect square on the left side:
(x + 3)(x + 3) = 57

Calculate the square root of the right side: 7.549834435

Break this problem into two subproblems by setting 
(x + 3) equal to 7.549834435 and -7.549834435.

Subproblem 1

x + 3 = 7.549834435 Simplifying x + 3 = 7.549834435 Reorder the terms: 3 + x = 7.549834435 Solving 3 + x = 7.549834435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 7.549834435 + -3 Combine like terms: 3 + -3 = 0 0 + x = 7.549834435 + -3 x = 7.549834435 + -3 Combine like terms: 7.549834435 + -3 = 4.549834435 x = 4.549834435 Simplifying x = 4.549834435

Subproblem 2

x + 3 = -7.549834435 Simplifying x + 3 = -7.549834435 Reorder the terms: 3 + x = -7.549834435 Solving 3 + x = -7.549834435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -7.549834435 + -3 Combine like terms: 3 + -3 = 0 0 + x = -7.549834435 + -3 x = -7.549834435 + -3 Combine like terms: -7.549834435 + -3 = -10.549834435 x = -10.549834435 Simplifying x = -10.549834435

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.549834435, -10.549834435}

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