(x^2+3x-4)+(3x-2)=

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Solution for (x^2+3x-4)+(3x-2)= equation:


Simplifying
(x2 + 3x + -4) + (3x + -2) = 0

Reorder the terms:
(-4 + 3x + x2) + (3x + -2) = 0

Remove parenthesis around (-4 + 3x + x2)
-4 + 3x + x2 + (3x + -2) = 0

Reorder the terms:
-4 + 3x + x2 + (-2 + 3x) = 0

Remove parenthesis around (-2 + 3x)
-4 + 3x + x2 + -2 + 3x = 0

Reorder the terms:
-4 + -2 + 3x + 3x + x2 = 0

Combine like terms: -4 + -2 = -6
-6 + 3x + 3x + x2 = 0

Combine like terms: 3x + 3x = 6x
-6 + 6x + x2 = 0

Solving
-6 + 6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = 6 + 9

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

Combine like terms: 6 + 9 = 15
9 + 6x + x2 = 15

Factor a perfect square on the left side:
(x + 3)(x + 3) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(x + 3) equal to 3.872983346 and -3.872983346.

Subproblem 1

x + 3 = 3.872983346 Simplifying x + 3 = 3.872983346 Reorder the terms: 3 + x = 3.872983346 Solving 3 + x = 3.872983346 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 = 3.872983346 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.872983346 + -3 x = 3.872983346 + -3 Combine like terms: 3.872983346 + -3 = 0.872983346 x = 0.872983346 Simplifying x = 0.872983346

Subproblem 2

x + 3 = -3.872983346 Simplifying x + 3 = -3.872983346 Reorder the terms: 3 + x = -3.872983346 Solving 3 + x = -3.872983346 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 = -3.872983346 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.872983346 + -3 x = -3.872983346 + -3 Combine like terms: -3.872983346 + -3 = -6.872983346 x = -6.872983346 Simplifying x = -6.872983346

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.872983346, -6.872983346}

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