x^2+35x+19=

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Solution for x^2+35x+19= equation:


Simplifying
x2 + 35x + 19 = 0

Reorder the terms:
19 + 35x + x2 = 0

Solving
19 + 35x + 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 + 35x + -19 + x2 = 0 + -19

Reorder the terms:
19 + -19 + 35x + x2 = 0 + -19

Combine like terms: 19 + -19 = 0
0 + 35x + x2 = 0 + -19
35x + x2 = 0 + -19

Combine like terms: 0 + -19 = -19
35x + x2 = -19

The x term is 35x.  Take half its coefficient (17.5).
Square it (306.25) and add it to both sides.

Add '306.25' to each side of the equation.
35x + 306.25 + x2 = -19 + 306.25

Reorder the terms:
306.25 + 35x + x2 = -19 + 306.25

Combine like terms: -19 + 306.25 = 287.25
306.25 + 35x + x2 = 287.25

Factor a perfect square on the left side:
(x + 17.5)(x + 17.5) = 287.25

Calculate the square root of the right side: 16.948451257

Break this problem into two subproblems by setting 
(x + 17.5) equal to 16.948451257 and -16.948451257.

Subproblem 1

x + 17.5 = 16.948451257 Simplifying x + 17.5 = 16.948451257 Reorder the terms: 17.5 + x = 16.948451257 Solving 17.5 + x = 16.948451257 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x = 16.948451257 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = 16.948451257 + -17.5 x = 16.948451257 + -17.5 Combine like terms: 16.948451257 + -17.5 = -0.551548743 x = -0.551548743 Simplifying x = -0.551548743

Subproblem 2

x + 17.5 = -16.948451257 Simplifying x + 17.5 = -16.948451257 Reorder the terms: 17.5 + x = -16.948451257 Solving 17.5 + x = -16.948451257 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x = -16.948451257 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = -16.948451257 + -17.5 x = -16.948451257 + -17.5 Combine like terms: -16.948451257 + -17.5 = -34.448451257 x = -34.448451257 Simplifying x = -34.448451257

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.551548743, -34.448451257}

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