(x-6)(x)=28

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Solution for (x-6)(x)=28 equation:


Simplifying
(x + -6)(x) = 28

Reorder the terms:
(-6 + x)(x) = 28

Reorder the terms for easier multiplication:
x(-6 + x) = 28
(-6 * x + x * x) = 28
(-6x + x2) = 28

Solving
-6x + x2 = 28

Solving for variable 'x'.

Reorder the terms:
-28 + -6x + x2 = 28 + -28

Combine like terms: 28 + -28 = 0
-28 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + -6x + 28 + x2 = 0 + 28

Reorder the terms:
-28 + 28 + -6x + x2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + -6x + x2 = 0 + 28
-6x + x2 = 0 + 28

Combine like terms: 0 + 28 = 28
-6x + x2 = 28

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 28 + 9

Reorder the terms:
9 + -6x + x2 = 28 + 9

Combine like terms: 28 + 9 = 37
9 + -6x + x2 = 37

Factor a perfect square on the left side:
(x + -3)(x + -3) = 37

Calculate the square root of the right side: 6.08276253

Break this problem into two subproblems by setting 
(x + -3) equal to 6.08276253 and -6.08276253.

Subproblem 1

x + -3 = 6.08276253 Simplifying x + -3 = 6.08276253 Reorder the terms: -3 + x = 6.08276253 Solving -3 + x = 6.08276253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 6.08276253 + 3 Combine like terms: -3 + 3 = 0 0 + x = 6.08276253 + 3 x = 6.08276253 + 3 Combine like terms: 6.08276253 + 3 = 9.08276253 x = 9.08276253 Simplifying x = 9.08276253

Subproblem 2

x + -3 = -6.08276253 Simplifying x + -3 = -6.08276253 Reorder the terms: -3 + x = -6.08276253 Solving -3 + x = -6.08276253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -6.08276253 + 3 Combine like terms: -3 + 3 = 0 0 + x = -6.08276253 + 3 x = -6.08276253 + 3 Combine like terms: -6.08276253 + 3 = -3.08276253 x = -3.08276253 Simplifying x = -3.08276253

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.08276253, -3.08276253}

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