x^2-9x-28=0

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Solution for x^2-9x-28=0 equation:


Simplifying
x2 + -9x + -28 = 0

Reorder the terms:
-28 + -9x + x2 = 0

Solving
-28 + -9x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + -9x + 28 + x2 = 0 + 28

Reorder the terms:
-28 + 28 + -9x + x2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + -9x + x2 = 0 + 28
-9x + x2 = 0 + 28

Combine like terms: 0 + 28 = 28
-9x + x2 = 28

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = 28 + 20.25

Reorder the terms:
20.25 + -9x + x2 = 28 + 20.25

Combine like terms: 28 + 20.25 = 48.25
20.25 + -9x + x2 = 48.25

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 48.25

Calculate the square root of the right side: 6.946221995

Break this problem into two subproblems by setting 
(x + -4.5) equal to 6.946221995 and -6.946221995.

Subproblem 1

x + -4.5 = 6.946221995 Simplifying x + -4.5 = 6.946221995 Reorder the terms: -4.5 + x = 6.946221995 Solving -4.5 + x = 6.946221995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 6.946221995 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 6.946221995 + 4.5 x = 6.946221995 + 4.5 Combine like terms: 6.946221995 + 4.5 = 11.446221995 x = 11.446221995 Simplifying x = 11.446221995

Subproblem 2

x + -4.5 = -6.946221995 Simplifying x + -4.5 = -6.946221995 Reorder the terms: -4.5 + x = -6.946221995 Solving -4.5 + x = -6.946221995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -6.946221995 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -6.946221995 + 4.5 x = -6.946221995 + 4.5 Combine like terms: -6.946221995 + 4.5 = -2.446221995 x = -2.446221995 Simplifying x = -2.446221995

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.446221995, -2.446221995}

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