x^2-22x-275=0

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Solution for x^2-22x-275=0 equation:


Simplifying
x2 + -22x + -275 = 0

Reorder the terms:
-275 + -22x + x2 = 0

Solving
-275 + -22x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '275' to each side of the equation.
-275 + -22x + 275 + x2 = 0 + 275

Reorder the terms:
-275 + 275 + -22x + x2 = 0 + 275

Combine like terms: -275 + 275 = 0
0 + -22x + x2 = 0 + 275
-22x + x2 = 0 + 275

Combine like terms: 0 + 275 = 275
-22x + x2 = 275

The x term is -22x.  Take half its coefficient (-11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
-22x + 121 + x2 = 275 + 121

Reorder the terms:
121 + -22x + x2 = 275 + 121

Combine like terms: 275 + 121 = 396
121 + -22x + x2 = 396

Factor a perfect square on the left side:
(x + -11)(x + -11) = 396

Calculate the square root of the right side: 19.899748742

Break this problem into two subproblems by setting 
(x + -11) equal to 19.899748742 and -19.899748742.

Subproblem 1

x + -11 = 19.899748742 Simplifying x + -11 = 19.899748742 Reorder the terms: -11 + x = 19.899748742 Solving -11 + x = 19.899748742 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = 19.899748742 + 11 Combine like terms: -11 + 11 = 0 0 + x = 19.899748742 + 11 x = 19.899748742 + 11 Combine like terms: 19.899748742 + 11 = 30.899748742 x = 30.899748742 Simplifying x = 30.899748742

Subproblem 2

x + -11 = -19.899748742 Simplifying x + -11 = -19.899748742 Reorder the terms: -11 + x = -19.899748742 Solving -11 + x = -19.899748742 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = -19.899748742 + 11 Combine like terms: -11 + 11 = 0 0 + x = -19.899748742 + 11 x = -19.899748742 + 11 Combine like terms: -19.899748742 + 11 = -8.899748742 x = -8.899748742 Simplifying x = -8.899748742

Solution

The solution to the problem is based on the solutions from the subproblems. x = {30.899748742, -8.899748742}

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