x^2+8x-19=0

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Solution for x^2+8x-19=0 equation:


Simplifying
x2 + 8x + -19 = 0

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

Solving
-19 + 8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '19' to each side of the equation.
-19 + 8x + 19 + x2 = 0 + 19

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

Combine like terms: -19 + 19 = 0
0 + 8x + x2 = 0 + 19
8x + x2 = 0 + 19

Combine like terms: 0 + 19 = 19
8x + x2 = 19

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 19 + 16

Reorder the terms:
16 + 8x + x2 = 19 + 16

Combine like terms: 19 + 16 = 35
16 + 8x + x2 = 35

Factor a perfect square on the left side:
(x + 4)(x + 4) = 35

Calculate the square root of the right side: 5.916079783

Break this problem into two subproblems by setting 
(x + 4) equal to 5.916079783 and -5.916079783.

Subproblem 1

x + 4 = 5.916079783 Simplifying x + 4 = 5.916079783 Reorder the terms: 4 + x = 5.916079783 Solving 4 + x = 5.916079783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 5.916079783 + -4 Combine like terms: 4 + -4 = 0 0 + x = 5.916079783 + -4 x = 5.916079783 + -4 Combine like terms: 5.916079783 + -4 = 1.916079783 x = 1.916079783 Simplifying x = 1.916079783

Subproblem 2

x + 4 = -5.916079783 Simplifying x + 4 = -5.916079783 Reorder the terms: 4 + x = -5.916079783 Solving 4 + x = -5.916079783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -5.916079783 + -4 Combine like terms: 4 + -4 = 0 0 + x = -5.916079783 + -4 x = -5.916079783 + -4 Combine like terms: -5.916079783 + -4 = -9.916079783 x = -9.916079783 Simplifying x = -9.916079783

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.916079783, -9.916079783}

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