50x^2+35x+4=0

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Solution for 50x^2+35x+4=0 equation:


Simplifying
50x2 + 35x + 4 = 0

Reorder the terms:
4 + 35x + 50x2 = 0

Solving
4 + 35x + 50x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
50 the coefficient of the squared term: 

Divide each side by '50'.
0.08 + 0.7x + x2 = 0

Move the constant term to the right:

Add '-0.08' to each side of the equation.
0.08 + 0.7x + -0.08 + x2 = 0 + -0.08

Reorder the terms:
0.08 + -0.08 + 0.7x + x2 = 0 + -0.08

Combine like terms: 0.08 + -0.08 = 0.00
0.00 + 0.7x + x2 = 0 + -0.08
0.7x + x2 = 0 + -0.08

Combine like terms: 0 + -0.08 = -0.08
0.7x + x2 = -0.08

The x term is 0.7x.  Take half its coefficient (0.35).
Square it (0.1225) and add it to both sides.

Add '0.1225' to each side of the equation.
0.7x + 0.1225 + x2 = -0.08 + 0.1225

Reorder the terms:
0.1225 + 0.7x + x2 = -0.08 + 0.1225

Combine like terms: -0.08 + 0.1225 = 0.0425
0.1225 + 0.7x + x2 = 0.0425

Factor a perfect square on the left side:
(x + 0.35)(x + 0.35) = 0.0425

Calculate the square root of the right side: 0.206155281

Break this problem into two subproblems by setting 
(x + 0.35) equal to 0.206155281 and -0.206155281.

Subproblem 1

x + 0.35 = 0.206155281 Simplifying x + 0.35 = 0.206155281 Reorder the terms: 0.35 + x = 0.206155281 Solving 0.35 + x = 0.206155281 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.35' to each side of the equation. 0.35 + -0.35 + x = 0.206155281 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + x = 0.206155281 + -0.35 x = 0.206155281 + -0.35 Combine like terms: 0.206155281 + -0.35 = -0.143844719 x = -0.143844719 Simplifying x = -0.143844719

Subproblem 2

x + 0.35 = -0.206155281 Simplifying x + 0.35 = -0.206155281 Reorder the terms: 0.35 + x = -0.206155281 Solving 0.35 + x = -0.206155281 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.35' to each side of the equation. 0.35 + -0.35 + x = -0.206155281 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + x = -0.206155281 + -0.35 x = -0.206155281 + -0.35 Combine like terms: -0.206155281 + -0.35 = -0.556155281 x = -0.556155281 Simplifying x = -0.556155281

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.143844719, -0.556155281}

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