x^2+19x-16=0

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Solution for x^2+19x-16=0 equation:


Simplifying
x2 + 19x + -16 = 0

Reorder the terms:
-16 + 19x + x2 = 0

Solving
-16 + 19x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 19x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + 19x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 19x + x2 = 0 + 16
19x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
19x + x2 = 16

The x term is 19x.  Take half its coefficient (9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
19x + 90.25 + x2 = 16 + 90.25

Reorder the terms:
90.25 + 19x + x2 = 16 + 90.25

Combine like terms: 16 + 90.25 = 106.25
90.25 + 19x + x2 = 106.25

Factor a perfect square on the left side:
(x + 9.5)(x + 9.5) = 106.25

Calculate the square root of the right side: 10.307764064

Break this problem into two subproblems by setting 
(x + 9.5) equal to 10.307764064 and -10.307764064.

Subproblem 1

x + 9.5 = 10.307764064 Simplifying x + 9.5 = 10.307764064 Reorder the terms: 9.5 + x = 10.307764064 Solving 9.5 + x = 10.307764064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = 10.307764064 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 10.307764064 + -9.5 x = 10.307764064 + -9.5 Combine like terms: 10.307764064 + -9.5 = 0.807764064 x = 0.807764064 Simplifying x = 0.807764064

Subproblem 2

x + 9.5 = -10.307764064 Simplifying x + 9.5 = -10.307764064 Reorder the terms: 9.5 + x = -10.307764064 Solving 9.5 + x = -10.307764064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = -10.307764064 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -10.307764064 + -9.5 x = -10.307764064 + -9.5 Combine like terms: -10.307764064 + -9.5 = -19.807764064 x = -19.807764064 Simplifying x = -19.807764064

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.807764064, -19.807764064}

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