5x(x-8)=6

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Solution for 5x(x-8)=6 equation:


Simplifying
5x(x + -8) = 6

Reorder the terms:
5x(-8 + x) = 6
(-8 * 5x + x * 5x) = 6
(-40x + 5x2) = 6

Solving
-40x + 5x2 = 6

Solving for variable 'x'.

Reorder the terms:
-6 + -40x + 5x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + -40x + 5x2 = 0

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

Divide each side by '5'.
-1.2 + -8x + x2 = 0

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + -8x + 1.2 + x2 = 0 + 1.2

Reorder the terms:
-1.2 + 1.2 + -8x + x2 = 0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + -8x + x2 = 0 + 1.2
-8x + x2 = 0 + 1.2

Combine like terms: 0 + 1.2 = 1.2
-8x + x2 = 1.2

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 1.2 + 16

Reorder the terms:
16 + -8x + x2 = 1.2 + 16

Combine like terms: 1.2 + 16 = 17.2
16 + -8x + x2 = 17.2

Factor a perfect square on the left side:
(x + -4)(x + -4) = 17.2

Calculate the square root of the right side: 4.147288271

Break this problem into two subproblems by setting 
(x + -4) equal to 4.147288271 and -4.147288271.

Subproblem 1

x + -4 = 4.147288271 Simplifying x + -4 = 4.147288271 Reorder the terms: -4 + x = 4.147288271 Solving -4 + x = 4.147288271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 4.147288271 + 4 Combine like terms: -4 + 4 = 0 0 + x = 4.147288271 + 4 x = 4.147288271 + 4 Combine like terms: 4.147288271 + 4 = 8.147288271 x = 8.147288271 Simplifying x = 8.147288271

Subproblem 2

x + -4 = -4.147288271 Simplifying x + -4 = -4.147288271 Reorder the terms: -4 + x = -4.147288271 Solving -4 + x = -4.147288271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -4.147288271 + 4 Combine like terms: -4 + 4 = 0 0 + x = -4.147288271 + 4 x = -4.147288271 + 4 Combine like terms: -4.147288271 + 4 = -0.147288271 x = -0.147288271 Simplifying x = -0.147288271

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.147288271, -0.147288271}

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