2*X*X+3X-213=329

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Solution for 2*X*X+3X-213=329 equation:


Simplifying
2X * X + 3X + -213 = 329

Multiply X * X
2X2 + 3X + -213 = 329

Reorder the terms:
-213 + 3X + 2X2 = 329

Solving
-213 + 3X + 2X2 = 329

Solving for variable 'X'.

Reorder the terms:
-213 + -329 + 3X + 2X2 = 329 + -329

Combine like terms: -213 + -329 = -542
-542 + 3X + 2X2 = 329 + -329

Combine like terms: 329 + -329 = 0
-542 + 3X + 2X2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-271 + 1.5X + X2 = 0

Move the constant term to the right:

Add '271' to each side of the equation.
-271 + 1.5X + 271 + X2 = 0 + 271

Reorder the terms:
-271 + 271 + 1.5X + X2 = 0 + 271

Combine like terms: -271 + 271 = 0
0 + 1.5X + X2 = 0 + 271
1.5X + X2 = 0 + 271

Combine like terms: 0 + 271 = 271
1.5X + X2 = 271

The X term is 1.5X.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5X + 0.5625 + X2 = 271 + 0.5625

Reorder the terms:
0.5625 + 1.5X + X2 = 271 + 0.5625

Combine like terms: 271 + 0.5625 = 271.5625
0.5625 + 1.5X + X2 = 271.5625

Factor a perfect square on the left side:
(X + 0.75)(X + 0.75) = 271.5625

Calculate the square root of the right side: 16.479153498

Break this problem into two subproblems by setting 
(X + 0.75) equal to 16.479153498 and -16.479153498.

Subproblem 1

X + 0.75 = 16.479153498 Simplifying X + 0.75 = 16.479153498 Reorder the terms: 0.75 + X = 16.479153498 Solving 0.75 + X = 16.479153498 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + X = 16.479153498 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + X = 16.479153498 + -0.75 X = 16.479153498 + -0.75 Combine like terms: 16.479153498 + -0.75 = 15.729153498 X = 15.729153498 Simplifying X = 15.729153498

Subproblem 2

X + 0.75 = -16.479153498 Simplifying X + 0.75 = -16.479153498 Reorder the terms: 0.75 + X = -16.479153498 Solving 0.75 + X = -16.479153498 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + X = -16.479153498 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + X = -16.479153498 + -0.75 X = -16.479153498 + -0.75 Combine like terms: -16.479153498 + -0.75 = -17.229153498 X = -17.229153498 Simplifying X = -17.229153498

Solution

The solution to the problem is based on the solutions from the subproblems. X = {15.729153498, -17.229153498}

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