5x^2-3x-160=0

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Solution for 5x^2-3x-160=0 equation:


Simplifying
5x2 + -3x + -160 = 0

Reorder the terms:
-160 + -3x + 5x2 = 0

Solving
-160 + -3x + 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'.
-32 + -0.6x + x2 = 0

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + -0.6x + 32 + x2 = 0 + 32

Reorder the terms:
-32 + 32 + -0.6x + x2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + -0.6x + x2 = 0 + 32
-0.6x + x2 = 0 + 32

Combine like terms: 0 + 32 = 32
-0.6x + x2 = 32

The x term is -0.6x.  Take half its coefficient (-0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
-0.6x + 0.09 + x2 = 32 + 0.09

Reorder the terms:
0.09 + -0.6x + x2 = 32 + 0.09

Combine like terms: 32 + 0.09 = 32.09
0.09 + -0.6x + x2 = 32.09

Factor a perfect square on the left side:
(x + -0.3)(x + -0.3) = 32.09

Calculate the square root of the right side: 5.664803615

Break this problem into two subproblems by setting 
(x + -0.3) equal to 5.664803615 and -5.664803615.

Subproblem 1

x + -0.3 = 5.664803615 Simplifying x + -0.3 = 5.664803615 Reorder the terms: -0.3 + x = 5.664803615 Solving -0.3 + x = 5.664803615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 5.664803615 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 5.664803615 + 0.3 x = 5.664803615 + 0.3 Combine like terms: 5.664803615 + 0.3 = 5.964803615 x = 5.964803615 Simplifying x = 5.964803615

Subproblem 2

x + -0.3 = -5.664803615 Simplifying x + -0.3 = -5.664803615 Reorder the terms: -0.3 + x = -5.664803615 Solving -0.3 + x = -5.664803615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -5.664803615 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -5.664803615 + 0.3 x = -5.664803615 + 0.3 Combine like terms: -5.664803615 + 0.3 = -5.364803615 x = -5.364803615 Simplifying x = -5.364803615

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.964803615, -5.364803615}

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