x^2-15x-550=0

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Solution for x^2-15x-550=0 equation:


Simplifying
x2 + -15x + -550 = 0

Reorder the terms:
-550 + -15x + x2 = 0

Solving
-550 + -15x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '550' to each side of the equation.
-550 + -15x + 550 + x2 = 0 + 550

Reorder the terms:
-550 + 550 + -15x + x2 = 0 + 550

Combine like terms: -550 + 550 = 0
0 + -15x + x2 = 0 + 550
-15x + x2 = 0 + 550

Combine like terms: 0 + 550 = 550
-15x + x2 = 550

The x term is -15x.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15x + 56.25 + x2 = 550 + 56.25

Reorder the terms:
56.25 + -15x + x2 = 550 + 56.25

Combine like terms: 550 + 56.25 = 606.25
56.25 + -15x + x2 = 606.25

Factor a perfect square on the left side:
(x + -7.5)(x + -7.5) = 606.25

Calculate the square root of the right side: 24.622144504

Break this problem into two subproblems by setting 
(x + -7.5) equal to 24.622144504 and -24.622144504.

Subproblem 1

x + -7.5 = 24.622144504 Simplifying x + -7.5 = 24.622144504 Reorder the terms: -7.5 + x = 24.622144504 Solving -7.5 + x = 24.622144504 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 24.622144504 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 24.622144504 + 7.5 x = 24.622144504 + 7.5 Combine like terms: 24.622144504 + 7.5 = 32.122144504 x = 32.122144504 Simplifying x = 32.122144504

Subproblem 2

x + -7.5 = -24.622144504 Simplifying x + -7.5 = -24.622144504 Reorder the terms: -7.5 + x = -24.622144504 Solving -7.5 + x = -24.622144504 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -24.622144504 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -24.622144504 + 7.5 x = -24.622144504 + 7.5 Combine like terms: -24.622144504 + 7.5 = -17.122144504 x = -17.122144504 Simplifying x = -17.122144504

Solution

The solution to the problem is based on the solutions from the subproblems. x = {32.122144504, -17.122144504}

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