x^2+35x+3=0

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Solution for x^2+35x+3=0 equation:


Simplifying
x2 + 35x + 3 = 0

Reorder the terms:
3 + 35x + x2 = 0

Solving
3 + 35x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 35x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + 35x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 35x + x2 = 0 + -3
35x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
35x + x2 = -3

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 = -3 + 306.25

Reorder the terms:
306.25 + 35x + x2 = -3 + 306.25

Combine like terms: -3 + 306.25 = 303.25
306.25 + 35x + x2 = 303.25

Factor a perfect square on the left side:
(x + 17.5)(x + 17.5) = 303.25

Calculate the square root of the right side: 17.414074767

Break this problem into two subproblems by setting 
(x + 17.5) equal to 17.414074767 and -17.414074767.

Subproblem 1

x + 17.5 = 17.414074767 Simplifying x + 17.5 = 17.414074767 Reorder the terms: 17.5 + x = 17.414074767 Solving 17.5 + x = 17.414074767 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 = 17.414074767 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = 17.414074767 + -17.5 x = 17.414074767 + -17.5 Combine like terms: 17.414074767 + -17.5 = -0.085925233 x = -0.085925233 Simplifying x = -0.085925233

Subproblem 2

x + 17.5 = -17.414074767 Simplifying x + 17.5 = -17.414074767 Reorder the terms: 17.5 + x = -17.414074767 Solving 17.5 + x = -17.414074767 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 = -17.414074767 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = -17.414074767 + -17.5 x = -17.414074767 + -17.5 Combine like terms: -17.414074767 + -17.5 = -34.914074767 x = -34.914074767 Simplifying x = -34.914074767

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.085925233, -34.914074767}

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