5x^2-35x-8=0

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Solution for 5x^2-35x-8=0 equation:


Simplifying
5x2 + -35x + -8 = 0

Reorder the terms:
-8 + -35x + 5x2 = 0

Solving
-8 + -35x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
-1.6 + -7x + x2 = 0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + -7x + 1.6 + x2 = 0 + 1.6

Reorder the terms:
-1.6 + 1.6 + -7x + x2 = 0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + -7x + x2 = 0 + 1.6
-7x + x2 = 0 + 1.6

Combine like terms: 0 + 1.6 = 1.6
-7x + x2 = 1.6

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = 1.6 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 1.6 + 12.25

Combine like terms: 1.6 + 12.25 = 13.85
12.25 + -7x + x2 = 13.85

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 13.85

Calculate the square root of the right side: 3.721558813

Break this problem into two subproblems by setting 
(x + -3.5) equal to 3.721558813 and -3.721558813.

Subproblem 1

x + -3.5 = 3.721558813 Simplifying x + -3.5 = 3.721558813 Reorder the terms: -3.5 + x = 3.721558813 Solving -3.5 + x = 3.721558813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 3.721558813 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.721558813 + 3.5 x = 3.721558813 + 3.5 Combine like terms: 3.721558813 + 3.5 = 7.221558813 x = 7.221558813 Simplifying x = 7.221558813

Subproblem 2

x + -3.5 = -3.721558813 Simplifying x + -3.5 = -3.721558813 Reorder the terms: -3.5 + x = -3.721558813 Solving -3.5 + x = -3.721558813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -3.721558813 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.721558813 + 3.5 x = -3.721558813 + 3.5 Combine like terms: -3.721558813 + 3.5 = -0.221558813 x = -0.221558813 Simplifying x = -0.221558813

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.221558813, -0.221558813}

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