x^2+8x-274=0

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Solution for x^2+8x-274=0 equation:


Simplifying
x2 + 8x + -274 = 0

Reorder the terms:
-274 + 8x + x2 = 0

Solving
-274 + 8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '274' to each side of the equation.
-274 + 8x + 274 + x2 = 0 + 274

Reorder the terms:
-274 + 274 + 8x + x2 = 0 + 274

Combine like terms: -274 + 274 = 0
0 + 8x + x2 = 0 + 274
8x + x2 = 0 + 274

Combine like terms: 0 + 274 = 274
8x + x2 = 274

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 274 + 16

Reorder the terms:
16 + 8x + x2 = 274 + 16

Combine like terms: 274 + 16 = 290
16 + 8x + x2 = 290

Factor a perfect square on the left side:
(x + 4)(x + 4) = 290

Calculate the square root of the right side: 17.029386366

Break this problem into two subproblems by setting 
(x + 4) equal to 17.029386366 and -17.029386366.

Subproblem 1

x + 4 = 17.029386366 Simplifying x + 4 = 17.029386366 Reorder the terms: 4 + x = 17.029386366 Solving 4 + x = 17.029386366 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 17.029386366 + -4 Combine like terms: 4 + -4 = 0 0 + x = 17.029386366 + -4 x = 17.029386366 + -4 Combine like terms: 17.029386366 + -4 = 13.029386366 x = 13.029386366 Simplifying x = 13.029386366

Subproblem 2

x + 4 = -17.029386366 Simplifying x + 4 = -17.029386366 Reorder the terms: 4 + x = -17.029386366 Solving 4 + x = -17.029386366 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -17.029386366 + -4 Combine like terms: 4 + -4 = 0 0 + x = -17.029386366 + -4 x = -17.029386366 + -4 Combine like terms: -17.029386366 + -4 = -21.029386366 x = -21.029386366 Simplifying x = -21.029386366

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.029386366, -21.029386366}

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