X^2+4X-232=0

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Solution for X^2+4X-232=0 equation:


Simplifying
X2 + 4X + -232 = 0

Reorder the terms:
-232 + 4X + X2 = 0

Solving
-232 + 4X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '232' to each side of the equation.
-232 + 4X + 232 + X2 = 0 + 232

Reorder the terms:
-232 + 232 + 4X + X2 = 0 + 232

Combine like terms: -232 + 232 = 0
0 + 4X + X2 = 0 + 232
4X + X2 = 0 + 232

Combine like terms: 0 + 232 = 232
4X + X2 = 232

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 = 232 + 4

Reorder the terms:
4 + 4X + X2 = 232 + 4

Combine like terms: 232 + 4 = 236
4 + 4X + X2 = 236

Factor a perfect square on the left side:
(X + 2)(X + 2) = 236

Calculate the square root of the right side: 15.362291496

Break this problem into two subproblems by setting 
(X + 2) equal to 15.362291496 and -15.362291496.

Subproblem 1

X + 2 = 15.362291496 Simplifying X + 2 = 15.362291496 Reorder the terms: 2 + X = 15.362291496 Solving 2 + X = 15.362291496 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 = 15.362291496 + -2 Combine like terms: 2 + -2 = 0 0 + X = 15.362291496 + -2 X = 15.362291496 + -2 Combine like terms: 15.362291496 + -2 = 13.362291496 X = 13.362291496 Simplifying X = 13.362291496

Subproblem 2

X + 2 = -15.362291496 Simplifying X + 2 = -15.362291496 Reorder the terms: 2 + X = -15.362291496 Solving 2 + X = -15.362291496 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 = -15.362291496 + -2 Combine like terms: 2 + -2 = 0 0 + X = -15.362291496 + -2 X = -15.362291496 + -2 Combine like terms: -15.362291496 + -2 = -17.362291496 X = -17.362291496 Simplifying X = -17.362291496

Solution

The solution to the problem is based on the solutions from the subproblems. X = {13.362291496, -17.362291496}

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