x=-x^2+12x+28

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Solution for x=-x^2+12x+28 equation:


Simplifying
x = -1x2 + 12x + 28

Reorder the terms:
x = 28 + 12x + -1x2

Solving
x = 28 + 12x + -1x2

Solving for variable 'x'.

Reorder the terms:
-28 + x + -12x + x2 = 28 + 12x + -1x2 + -28 + -12x + x2

Combine like terms: x + -12x = -11x
-28 + -11x + x2 = 28 + 12x + -1x2 + -28 + -12x + x2

Reorder the terms:
-28 + -11x + x2 = 28 + -28 + 12x + -12x + -1x2 + x2

Combine like terms: 28 + -28 = 0
-28 + -11x + x2 = 0 + 12x + -12x + -1x2 + x2
-28 + -11x + x2 = 12x + -12x + -1x2 + x2

Combine like terms: 12x + -12x = 0
-28 + -11x + x2 = 0 + -1x2 + x2
-28 + -11x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-28 + -11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + -11x + 28 + x2 = 0 + 28

Reorder the terms:
-28 + 28 + -11x + x2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + -11x + x2 = 0 + 28
-11x + x2 = 0 + 28

Combine like terms: 0 + 28 = 28
-11x + x2 = 28

The x term is -11x.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11x + 30.25 + x2 = 28 + 30.25

Reorder the terms:
30.25 + -11x + x2 = 28 + 30.25

Combine like terms: 28 + 30.25 = 58.25
30.25 + -11x + x2 = 58.25

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 58.25

Calculate the square root of the right side: 7.632168761

Break this problem into two subproblems by setting 
(x + -5.5) equal to 7.632168761 and -7.632168761.

Subproblem 1

x + -5.5 = 7.632168761 Simplifying x + -5.5 = 7.632168761 Reorder the terms: -5.5 + x = 7.632168761 Solving -5.5 + x = 7.632168761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 7.632168761 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 7.632168761 + 5.5 x = 7.632168761 + 5.5 Combine like terms: 7.632168761 + 5.5 = 13.132168761 x = 13.132168761 Simplifying x = 13.132168761

Subproblem 2

x + -5.5 = -7.632168761 Simplifying x + -5.5 = -7.632168761 Reorder the terms: -5.5 + x = -7.632168761 Solving -5.5 + x = -7.632168761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -7.632168761 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -7.632168761 + 5.5 x = -7.632168761 + 5.5 Combine like terms: -7.632168761 + 5.5 = -2.132168761 x = -2.132168761 Simplifying x = -2.132168761

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.132168761, -2.132168761}

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