X^2+4X=105

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Solution for X^2+4X=105 equation:


Simplifying
X2 + 4X = 105

Reorder the terms:
4X + X2 = 105

Solving
4X + X2 = 105

Solving for variable 'X'.

Reorder the terms:
-105 + 4X + X2 = 105 + -105

Combine like terms: 105 + -105 = 0
-105 + 4X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '105' to each side of the equation.
-105 + 4X + 105 + X2 = 0 + 105

Reorder the terms:
-105 + 105 + 4X + X2 = 0 + 105

Combine like terms: -105 + 105 = 0
0 + 4X + X2 = 0 + 105
4X + X2 = 0 + 105

Combine like terms: 0 + 105 = 105
4X + X2 = 105

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 = 105 + 4

Reorder the terms:
4 + 4X + X2 = 105 + 4

Combine like terms: 105 + 4 = 109
4 + 4X + X2 = 109

Factor a perfect square on the left side:
(X + 2)(X + 2) = 109

Calculate the square root of the right side: 10.440306509

Break this problem into two subproblems by setting 
(X + 2) equal to 10.440306509 and -10.440306509.

Subproblem 1

X + 2 = 10.440306509 Simplifying X + 2 = 10.440306509 Reorder the terms: 2 + X = 10.440306509 Solving 2 + X = 10.440306509 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 = 10.440306509 + -2 Combine like terms: 2 + -2 = 0 0 + X = 10.440306509 + -2 X = 10.440306509 + -2 Combine like terms: 10.440306509 + -2 = 8.440306509 X = 8.440306509 Simplifying X = 8.440306509

Subproblem 2

X + 2 = -10.440306509 Simplifying X + 2 = -10.440306509 Reorder the terms: 2 + X = -10.440306509 Solving 2 + X = -10.440306509 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 = -10.440306509 + -2 Combine like terms: 2 + -2 = 0 0 + X = -10.440306509 + -2 X = -10.440306509 + -2 Combine like terms: -10.440306509 + -2 = -12.440306509 X = -12.440306509 Simplifying X = -12.440306509

Solution

The solution to the problem is based on the solutions from the subproblems. X = {8.440306509, -12.440306509}

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