3x^2+18x-94=3

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Solution for 3x^2+18x-94=3 equation:


Simplifying
3x2 + 18x + -94 = 3

Reorder the terms:
-94 + 18x + 3x2 = 3

Solving
-94 + 18x + 3x2 = 3

Solving for variable 'x'.

Reorder the terms:
-94 + -3 + 18x + 3x2 = 3 + -3

Combine like terms: -94 + -3 = -97
-97 + 18x + 3x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-97 + 18x + 3x2 = 0

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

Divide each side by '3'.
-32.33333333 + 6x + x2 = 0

Move the constant term to the right:

Add '32.33333333' to each side of the equation.
-32.33333333 + 6x + 32.33333333 + x2 = 0 + 32.33333333

Reorder the terms:
-32.33333333 + 32.33333333 + 6x + x2 = 0 + 32.33333333

Combine like terms: -32.33333333 + 32.33333333 = 0.00000000
0.00000000 + 6x + x2 = 0 + 32.33333333
6x + x2 = 0 + 32.33333333

Combine like terms: 0 + 32.33333333 = 32.33333333
6x + x2 = 32.33333333

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 32.33333333 + 9

Reorder the terms:
9 + 6x + x2 = 32.33333333 + 9

Combine like terms: 32.33333333 + 9 = 41.33333333
9 + 6x + x2 = 41.33333333

Factor a perfect square on the left side:
(x + 3)(x + 3) = 41.33333333

Calculate the square root of the right side: 6.429100507

Break this problem into two subproblems by setting 
(x + 3) equal to 6.429100507 and -6.429100507.

Subproblem 1

x + 3 = 6.429100507 Simplifying x + 3 = 6.429100507 Reorder the terms: 3 + x = 6.429100507 Solving 3 + x = 6.429100507 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 6.429100507 + -3 Combine like terms: 3 + -3 = 0 0 + x = 6.429100507 + -3 x = 6.429100507 + -3 Combine like terms: 6.429100507 + -3 = 3.429100507 x = 3.429100507 Simplifying x = 3.429100507

Subproblem 2

x + 3 = -6.429100507 Simplifying x + 3 = -6.429100507 Reorder the terms: 3 + x = -6.429100507 Solving 3 + x = -6.429100507 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -6.429100507 + -3 Combine like terms: 3 + -3 = 0 0 + x = -6.429100507 + -3 x = -6.429100507 + -3 Combine like terms: -6.429100507 + -3 = -9.429100507 x = -9.429100507 Simplifying x = -9.429100507

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.429100507, -9.429100507}

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