3X+X^2-17=0

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Solution for 3X+X^2-17=0 equation:


Simplifying
3X + X2 + -17 = 0

Reorder the terms:
-17 + 3X + X2 = 0

Solving
-17 + 3X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + 3X + 17 + X2 = 0 + 17

Reorder the terms:
-17 + 17 + 3X + X2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + 3X + X2 = 0 + 17
3X + X2 = 0 + 17

Combine like terms: 0 + 17 = 17
3X + X2 = 17

The X term is 3X.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3X + 2.25 + X2 = 17 + 2.25

Reorder the terms:
2.25 + 3X + X2 = 17 + 2.25

Combine like terms: 17 + 2.25 = 19.25
2.25 + 3X + X2 = 19.25

Factor a perfect square on the left side:
(X + 1.5)(X + 1.5) = 19.25

Calculate the square root of the right side: 4.387482194

Break this problem into two subproblems by setting 
(X + 1.5) equal to 4.387482194 and -4.387482194.

Subproblem 1

X + 1.5 = 4.387482194 Simplifying X + 1.5 = 4.387482194 Reorder the terms: 1.5 + X = 4.387482194 Solving 1.5 + X = 4.387482194 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + X = 4.387482194 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + X = 4.387482194 + -1.5 X = 4.387482194 + -1.5 Combine like terms: 4.387482194 + -1.5 = 2.887482194 X = 2.887482194 Simplifying X = 2.887482194

Subproblem 2

X + 1.5 = -4.387482194 Simplifying X + 1.5 = -4.387482194 Reorder the terms: 1.5 + X = -4.387482194 Solving 1.5 + X = -4.387482194 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + X = -4.387482194 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + X = -4.387482194 + -1.5 X = -4.387482194 + -1.5 Combine like terms: -4.387482194 + -1.5 = -5.887482194 X = -5.887482194 Simplifying X = -5.887482194

Solution

The solution to the problem is based on the solutions from the subproblems. X = {2.887482194, -5.887482194}

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