x^2+4x-361=0

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Solution for x^2+4x-361=0 equation:


Simplifying
x2 + 4x + -361 = 0

Reorder the terms:
-361 + 4x + x2 = 0

Solving
-361 + 4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '361' to each side of the equation.
-361 + 4x + 361 + x2 = 0 + 361

Reorder the terms:
-361 + 361 + 4x + x2 = 0 + 361

Combine like terms: -361 + 361 = 0
0 + 4x + x2 = 0 + 361
4x + x2 = 0 + 361

Combine like terms: 0 + 361 = 361
4x + x2 = 361

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 361 + 4

Reorder the terms:
4 + 4x + x2 = 361 + 4

Combine like terms: 361 + 4 = 365
4 + 4x + x2 = 365

Factor a perfect square on the left side:
(x + 2)(x + 2) = 365

Calculate the square root of the right side: 19.104973175

Break this problem into two subproblems by setting 
(x + 2) equal to 19.104973175 and -19.104973175.

Subproblem 1

x + 2 = 19.104973175 Simplifying x + 2 = 19.104973175 Reorder the terms: 2 + x = 19.104973175 Solving 2 + x = 19.104973175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 19.104973175 + -2 Combine like terms: 2 + -2 = 0 0 + x = 19.104973175 + -2 x = 19.104973175 + -2 Combine like terms: 19.104973175 + -2 = 17.104973175 x = 17.104973175 Simplifying x = 17.104973175

Subproblem 2

x + 2 = -19.104973175 Simplifying x + 2 = -19.104973175 Reorder the terms: 2 + x = -19.104973175 Solving 2 + x = -19.104973175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -19.104973175 + -2 Combine like terms: 2 + -2 = 0 0 + x = -19.104973175 + -2 x = -19.104973175 + -2 Combine like terms: -19.104973175 + -2 = -21.104973175 x = -21.104973175 Simplifying x = -21.104973175

Solution

The solution to the problem is based on the solutions from the subproblems. x = {17.104973175, -21.104973175}

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