2x^2+5x+12=19-7x

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Solution for 2x^2+5x+12=19-7x equation:


Simplifying
2x2 + 5x + 12 = 19 + -7x

Reorder the terms:
12 + 5x + 2x2 = 19 + -7x

Solving
12 + 5x + 2x2 = 19 + -7x

Solving for variable 'x'.

Reorder the terms:
12 + -19 + 5x + 7x + 2x2 = 19 + -7x + -19 + 7x

Combine like terms: 12 + -19 = -7
-7 + 5x + 7x + 2x2 = 19 + -7x + -19 + 7x

Combine like terms: 5x + 7x = 12x
-7 + 12x + 2x2 = 19 + -7x + -19 + 7x

Reorder the terms:
-7 + 12x + 2x2 = 19 + -19 + -7x + 7x

Combine like terms: 19 + -19 = 0
-7 + 12x + 2x2 = 0 + -7x + 7x
-7 + 12x + 2x2 = -7x + 7x

Combine like terms: -7x + 7x = 0
-7 + 12x + 2x2 = 0

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

Divide each side by '2'.
-3.5 + 6x + x2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + 6x + 3.5 + x2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + 6x + x2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + 6x + x2 = 0 + 3.5
6x + x2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
6x + x2 = 3.5

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 = 3.5 + 9

Reorder the terms:
9 + 6x + x2 = 3.5 + 9

Combine like terms: 3.5 + 9 = 12.5
9 + 6x + x2 = 12.5

Factor a perfect square on the left side:
(x + 3)(x + 3) = 12.5

Calculate the square root of the right side: 3.535533906

Break this problem into two subproblems by setting 
(x + 3) equal to 3.535533906 and -3.535533906.

Subproblem 1

x + 3 = 3.535533906 Simplifying x + 3 = 3.535533906 Reorder the terms: 3 + x = 3.535533906 Solving 3 + x = 3.535533906 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 = 3.535533906 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.535533906 + -3 x = 3.535533906 + -3 Combine like terms: 3.535533906 + -3 = 0.535533906 x = 0.535533906 Simplifying x = 0.535533906

Subproblem 2

x + 3 = -3.535533906 Simplifying x + 3 = -3.535533906 Reorder the terms: 3 + x = -3.535533906 Solving 3 + x = -3.535533906 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 = -3.535533906 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.535533906 + -3 x = -3.535533906 + -3 Combine like terms: -3.535533906 + -3 = -6.535533906 x = -6.535533906 Simplifying x = -6.535533906

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.535533906, -6.535533906}

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