x^2+8x=309

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Solution for x^2+8x=309 equation:


Simplifying
x2 + 8x = 309

Reorder the terms:
8x + x2 = 309

Solving
8x + x2 = 309

Solving for variable 'x'.

Reorder the terms:
-309 + 8x + x2 = 309 + -309

Combine like terms: 309 + -309 = 0
-309 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '309' to each side of the equation.
-309 + 8x + 309 + x2 = 0 + 309

Reorder the terms:
-309 + 309 + 8x + x2 = 0 + 309

Combine like terms: -309 + 309 = 0
0 + 8x + x2 = 0 + 309
8x + x2 = 0 + 309

Combine like terms: 0 + 309 = 309
8x + x2 = 309

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 = 309 + 16

Reorder the terms:
16 + 8x + x2 = 309 + 16

Combine like terms: 309 + 16 = 325
16 + 8x + x2 = 325

Factor a perfect square on the left side:
(x + 4)(x + 4) = 325

Calculate the square root of the right side: 18.027756377

Break this problem into two subproblems by setting 
(x + 4) equal to 18.027756377 and -18.027756377.

Subproblem 1

x + 4 = 18.027756377 Simplifying x + 4 = 18.027756377 Reorder the terms: 4 + x = 18.027756377 Solving 4 + x = 18.027756377 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 = 18.027756377 + -4 Combine like terms: 4 + -4 = 0 0 + x = 18.027756377 + -4 x = 18.027756377 + -4 Combine like terms: 18.027756377 + -4 = 14.027756377 x = 14.027756377 Simplifying x = 14.027756377

Subproblem 2

x + 4 = -18.027756377 Simplifying x + 4 = -18.027756377 Reorder the terms: 4 + x = -18.027756377 Solving 4 + x = -18.027756377 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 = -18.027756377 + -4 Combine like terms: 4 + -4 = 0 0 + x = -18.027756377 + -4 x = -18.027756377 + -4 Combine like terms: -18.027756377 + -4 = -22.027756377 x = -22.027756377 Simplifying x = -22.027756377

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.027756377, -22.027756377}

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