x^2-20x+12=0

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Solution for x^2-20x+12=0 equation:


Simplifying
x2 + -20x + 12 = 0

Reorder the terms:
12 + -20x + x2 = 0

Solving
12 + -20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + -20x + -12 + x2 = 0 + -12

Reorder the terms:
12 + -12 + -20x + x2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -20x + x2 = 0 + -12
-20x + x2 = 0 + -12

Combine like terms: 0 + -12 = -12
-20x + x2 = -12

The x term is -20x.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x + 100 + x2 = -12 + 100

Reorder the terms:
100 + -20x + x2 = -12 + 100

Combine like terms: -12 + 100 = 88
100 + -20x + x2 = 88

Factor a perfect square on the left side:
(x + -10)(x + -10) = 88

Calculate the square root of the right side: 9.38083152

Break this problem into two subproblems by setting 
(x + -10) equal to 9.38083152 and -9.38083152.

Subproblem 1

x + -10 = 9.38083152 Simplifying x + -10 = 9.38083152 Reorder the terms: -10 + x = 9.38083152 Solving -10 + x = 9.38083152 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 9.38083152 + 10 Combine like terms: -10 + 10 = 0 0 + x = 9.38083152 + 10 x = 9.38083152 + 10 Combine like terms: 9.38083152 + 10 = 19.38083152 x = 19.38083152 Simplifying x = 19.38083152

Subproblem 2

x + -10 = -9.38083152 Simplifying x + -10 = -9.38083152 Reorder the terms: -10 + x = -9.38083152 Solving -10 + x = -9.38083152 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -9.38083152 + 10 Combine like terms: -10 + 10 = 0 0 + x = -9.38083152 + 10 x = -9.38083152 + 10 Combine like terms: -9.38083152 + 10 = 0.61916848 x = 0.61916848 Simplifying x = 0.61916848

Solution

The solution to the problem is based on the solutions from the subproblems. x = {19.38083152, 0.61916848}

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