5X^2-6X-160=0

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Solution for 5X^2-6X-160=0 equation:


Simplifying
5X2 + -6X + -160 = 0

Reorder the terms:
-160 + -6X + 5X2 = 0

Solving
-160 + -6X + 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 + -1.2X + X2 = 0

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + -1.2X + 32 + X2 = 0 + 32

Reorder the terms:
-32 + 32 + -1.2X + X2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + -1.2X + X2 = 0 + 32
-1.2X + X2 = 0 + 32

Combine like terms: 0 + 32 = 32
-1.2X + X2 = 32

The X term is -1.2X.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2X + 0.36 + X2 = 32 + 0.36

Reorder the terms:
0.36 + -1.2X + X2 = 32 + 0.36

Combine like terms: 32 + 0.36 = 32.36
0.36 + -1.2X + X2 = 32.36

Factor a perfect square on the left side:
(X + -0.6)(X + -0.6) = 32.36

Calculate the square root of the right side: 5.688585061

Break this problem into two subproblems by setting 
(X + -0.6) equal to 5.688585061 and -5.688585061.

Subproblem 1

X + -0.6 = 5.688585061 Simplifying X + -0.6 = 5.688585061 Reorder the terms: -0.6 + X = 5.688585061 Solving -0.6 + X = 5.688585061 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + X = 5.688585061 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + X = 5.688585061 + 0.6 X = 5.688585061 + 0.6 Combine like terms: 5.688585061 + 0.6 = 6.288585061 X = 6.288585061 Simplifying X = 6.288585061

Subproblem 2

X + -0.6 = -5.688585061 Simplifying X + -0.6 = -5.688585061 Reorder the terms: -0.6 + X = -5.688585061 Solving -0.6 + X = -5.688585061 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + X = -5.688585061 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + X = -5.688585061 + 0.6 X = -5.688585061 + 0.6 Combine like terms: -5.688585061 + 0.6 = -5.088585061 X = -5.088585061 Simplifying X = -5.088585061

Solution

The solution to the problem is based on the solutions from the subproblems. X = {6.288585061, -5.088585061}

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