2x^2+8x-19=

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Solution for 2x^2+8x-19= equation:


Simplifying
2x2 + 8x + -19 = 0

Reorder the terms:
-19 + 8x + 2x2 = 0

Solving
-19 + 8x + 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'.
-9.5 + 4x + x2 = 0

Move the constant term to the right:

Add '9.5' to each side of the equation.
-9.5 + 4x + 9.5 + x2 = 0 + 9.5

Reorder the terms:
-9.5 + 9.5 + 4x + x2 = 0 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + 4x + x2 = 0 + 9.5
4x + x2 = 0 + 9.5

Combine like terms: 0 + 9.5 = 9.5
4x + x2 = 9.5

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 9.5 + 4

Reorder the terms:
4 + 4x + x2 = 9.5 + 4

Combine like terms: 9.5 + 4 = 13.5
4 + 4x + x2 = 13.5

Factor a perfect square on the left side:
(x + 2)(x + 2) = 13.5

Calculate the square root of the right side: 3.674234614

Break this problem into two subproblems by setting 
(x + 2) equal to 3.674234614 and -3.674234614.

Subproblem 1

x + 2 = 3.674234614 Simplifying x + 2 = 3.674234614 Reorder the terms: 2 + x = 3.674234614 Solving 2 + x = 3.674234614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 3.674234614 + -2 Combine like terms: 2 + -2 = 0 0 + x = 3.674234614 + -2 x = 3.674234614 + -2 Combine like terms: 3.674234614 + -2 = 1.674234614 x = 1.674234614 Simplifying x = 1.674234614

Subproblem 2

x + 2 = -3.674234614 Simplifying x + 2 = -3.674234614 Reorder the terms: 2 + x = -3.674234614 Solving 2 + x = -3.674234614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -3.674234614 + -2 Combine like terms: 2 + -2 = 0 0 + x = -3.674234614 + -2 x = -3.674234614 + -2 Combine like terms: -3.674234614 + -2 = -5.674234614 x = -5.674234614 Simplifying x = -5.674234614

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.674234614, -5.674234614}

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