x^2+3x+4+x^2+2x-6=

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Solution for x^2+3x+4+x^2+2x-6= equation:


Simplifying
x2 + 3x + 4 + x2 + 2x + -6 = 0

Reorder the terms:
4 + -6 + 3x + 2x + x2 + x2 = 0

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

Combine like terms: 3x + 2x = 5x
-2 + 5x + x2 + x2 = 0

Combine like terms: x2 + x2 = 2x2
-2 + 5x + 2x2 = 0

Solving
-2 + 5x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-1 + 2.5x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 2.5x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 2.5x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2.5x + x2 = 0 + 1
2.5x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
2.5x + x2 = 1

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 1 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 1 + 1.5625

Combine like terms: 1 + 1.5625 = 2.5625
1.5625 + 2.5x + x2 = 2.5625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 2.5625

Calculate the square root of the right side: 1.600781059

Break this problem into two subproblems by setting 
(x + 1.25) equal to 1.600781059 and -1.600781059.

Subproblem 1

x + 1.25 = 1.600781059 Simplifying x + 1.25 = 1.600781059 Reorder the terms: 1.25 + x = 1.600781059 Solving 1.25 + x = 1.600781059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 1.600781059 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 1.600781059 + -1.25 x = 1.600781059 + -1.25 Combine like terms: 1.600781059 + -1.25 = 0.350781059 x = 0.350781059 Simplifying x = 0.350781059

Subproblem 2

x + 1.25 = -1.600781059 Simplifying x + 1.25 = -1.600781059 Reorder the terms: 1.25 + x = -1.600781059 Solving 1.25 + x = -1.600781059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -1.600781059 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -1.600781059 + -1.25 x = -1.600781059 + -1.25 Combine like terms: -1.600781059 + -1.25 = -2.850781059 x = -2.850781059 Simplifying x = -2.850781059

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.350781059, -2.850781059}

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