-0.67(x^2-12x+36)+7=0

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Solution for -0.67(x^2-12x+36)+7=0 equation:


Simplifying
-0.67(x2 + -12x + 36) + 7 = 0

Reorder the terms:
-0.67(36 + -12x + x2) + 7 = 0
(36 * -0.67 + -12x * -0.67 + x2 * -0.67) + 7 = 0
(-24.12 + 8.04x + -0.67x2) + 7 = 0

Reorder the terms:
-24.12 + 7 + 8.04x + -0.67x2 = 0

Combine like terms: -24.12 + 7 = -17.12
-17.12 + 8.04x + -0.67x2 = 0

Solving
-17.12 + 8.04x + -0.67x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.67 the coefficient of the squared term: 

Divide each side by '-0.67'.
25.55223881 + -12x + x2 = 0

Move the constant term to the right:

Add '-25.55223881' to each side of the equation.
25.55223881 + -12x + -25.55223881 + x2 = 0 + -25.55223881

Reorder the terms:
25.55223881 + -25.55223881 + -12x + x2 = 0 + -25.55223881

Combine like terms: 25.55223881 + -25.55223881 = 0.00000000
0.00000000 + -12x + x2 = 0 + -25.55223881
-12x + x2 = 0 + -25.55223881

Combine like terms: 0 + -25.55223881 = -25.55223881
-12x + x2 = -25.55223881

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = -25.55223881 + 36

Reorder the terms:
36 + -12x + x2 = -25.55223881 + 36

Combine like terms: -25.55223881 + 36 = 10.44776119
36 + -12x + x2 = 10.44776119

Factor a perfect square on the left side:
(x + -6)(x + -6) = 10.44776119

Calculate the square root of the right side: 3.232299675

Break this problem into two subproblems by setting 
(x + -6) equal to 3.232299675 and -3.232299675.

Subproblem 1

x + -6 = 3.232299675 Simplifying x + -6 = 3.232299675 Reorder the terms: -6 + x = 3.232299675 Solving -6 + x = 3.232299675 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 3.232299675 + 6 Combine like terms: -6 + 6 = 0 0 + x = 3.232299675 + 6 x = 3.232299675 + 6 Combine like terms: 3.232299675 + 6 = 9.232299675 x = 9.232299675 Simplifying x = 9.232299675

Subproblem 2

x + -6 = -3.232299675 Simplifying x + -6 = -3.232299675 Reorder the terms: -6 + x = -3.232299675 Solving -6 + x = -3.232299675 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -3.232299675 + 6 Combine like terms: -6 + 6 = 0 0 + x = -3.232299675 + 6 x = -3.232299675 + 6 Combine like terms: -3.232299675 + 6 = 2.767700325 x = 2.767700325 Simplifying x = 2.767700325

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.232299675, 2.767700325}

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