x^2-7x-73=0

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Solution for x^2-7x-73=0 equation:


Simplifying
x2 + -7x + -73 = 0

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

Solving
-73 + -7x + x2 = 0

Solving for variable 'x'.

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 = 12.733092656 x = 12.733092656 Simplifying x = 12.733092656

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 = -5.733092656 x = -5.733092656 Simplifying x = -5.733092656

Solution

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

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