x(x+7)=73

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Solution for x(x+7)=73 equation:


Simplifying
x(x + 7) = 73

Reorder the terms:
x(7 + x) = 73
(7 * x + x * x) = 73
(7x + x2) = 73

Solving
7x + x2 = 73

Solving for variable 'x'.

Reorder the terms:
-73 + 7x + x2 = 73 + -73

Combine like terms: 73 + -73 = 0
-73 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '73' to each side of the equation.
-73 + 7x + 73 + x2 = 0 + 73

Reorder the terms:
-73 + 73 + 7x + x2 = 0 + 73

Combine like terms: -73 + 73 = 0
0 + 7x + x2 = 0 + 73
7x + x2 = 0 + 73

Combine like terms: 0 + 73 = 73
7x + x2 = 73

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 73 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 73 + 12.25

Combine like terms: 73 + 12.25 = 85.25
12.25 + 7x + x2 = 85.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 85.25

Calculate the square root of the right side: 9.233092656

Break this problem into two subproblems by setting 
(x + 3.5) equal to 9.233092656 and -9.233092656.

Subproblem 1

x + 3.5 = 9.233092656 Simplifying x + 3.5 = 9.233092656 Reorder the terms: 3.5 + x = 9.233092656 Solving 3.5 + x = 9.233092656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 9.233092656 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 9.233092656 + -3.5 x = 9.233092656 + -3.5 Combine like terms: 9.233092656 + -3.5 = 5.733092656 x = 5.733092656 Simplifying x = 5.733092656

Subproblem 2

x + 3.5 = -9.233092656 Simplifying x + 3.5 = -9.233092656 Reorder the terms: 3.5 + x = -9.233092656 Solving 3.5 + x = -9.233092656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -9.233092656 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -9.233092656 + -3.5 x = -9.233092656 + -3.5 Combine like terms: -9.233092656 + -3.5 = -12.733092656 x = -12.733092656 Simplifying x = -12.733092656

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.733092656, -12.733092656}

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