0=x^2-16x-28

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Solution for 0=x^2-16x-28 equation:


Simplifying
0 = x2 + -16x + -28

Reorder the terms:
0 = -28 + -16x + x2

Solving
0 = -28 + -16x + x2

Solving for variable 'x'.

Combine like terms: 0 + 28 = 28
28 + 16x + -1x2 = -28 + -16x + x2 + 28 + 16x + -1x2

Reorder the terms:
28 + 16x + -1x2 = -28 + 28 + -16x + 16x + x2 + -1x2

Combine like terms: -28 + 28 = 0
28 + 16x + -1x2 = 0 + -16x + 16x + x2 + -1x2
28 + 16x + -1x2 = -16x + 16x + x2 + -1x2

Combine like terms: -16x + 16x = 0
28 + 16x + -1x2 = 0 + x2 + -1x2
28 + 16x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
28 + 16x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-28 + -16x + x2 = 0

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + -16x + 28 + x2 = 0 + 28

Reorder the terms:
-28 + 28 + -16x + x2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + -16x + x2 = 0 + 28
-16x + x2 = 0 + 28

Combine like terms: 0 + 28 = 28
-16x + x2 = 28

The x term is -16x.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16x + 64 + x2 = 28 + 64

Reorder the terms:
64 + -16x + x2 = 28 + 64

Combine like terms: 28 + 64 = 92
64 + -16x + x2 = 92

Factor a perfect square on the left side:
(x + -8)(x + -8) = 92

Calculate the square root of the right side: 9.591663047

Break this problem into two subproblems by setting 
(x + -8) equal to 9.591663047 and -9.591663047.

Subproblem 1

x + -8 = 9.591663047 Simplifying x + -8 = 9.591663047 Reorder the terms: -8 + x = 9.591663047 Solving -8 + x = 9.591663047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 9.591663047 + 8 Combine like terms: -8 + 8 = 0 0 + x = 9.591663047 + 8 x = 9.591663047 + 8 Combine like terms: 9.591663047 + 8 = 17.591663047 x = 17.591663047 Simplifying x = 17.591663047

Subproblem 2

x + -8 = -9.591663047 Simplifying x + -8 = -9.591663047 Reorder the terms: -8 + x = -9.591663047 Solving -8 + x = -9.591663047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -9.591663047 + 8 Combine like terms: -8 + 8 = 0 0 + x = -9.591663047 + 8 x = -9.591663047 + 8 Combine like terms: -9.591663047 + 8 = -1.591663047 x = -1.591663047 Simplifying x = -1.591663047

Solution

The solution to the problem is based on the solutions from the subproblems. x = {17.591663047, -1.591663047}

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