(m^2-10m+12)=0

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Solution for (m^2-10m+12)=0 equation:


Simplifying
(m2 + -10m + 12) = 0

Reorder the terms:
(12 + -10m + m2) = 0

Remove parenthesis around (12 + -10m + m2)
12 + -10m + m2 = 0

Solving
12 + -10m + m2 = 0

Solving for variable 'm'.

Begin completing the square.

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + -10m + -12 + m2 = 0 + -12

Reorder the terms:
12 + -12 + -10m + m2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -10m + m2 = 0 + -12
-10m + m2 = 0 + -12

Combine like terms: 0 + -12 = -12
-10m + m2 = -12

The m term is -10m.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10m + 25 + m2 = -12 + 25

Reorder the terms:
25 + -10m + m2 = -12 + 25

Combine like terms: -12 + 25 = 13
25 + -10m + m2 = 13

Factor a perfect square on the left side:
(m + -5)(m + -5) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(m + -5) equal to 3.605551275 and -3.605551275.

Subproblem 1

m + -5 = 3.605551275 Simplifying m + -5 = 3.605551275 Reorder the terms: -5 + m = 3.605551275 Solving -5 + m = 3.605551275 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + m = 3.605551275 + 5 Combine like terms: -5 + 5 = 0 0 + m = 3.605551275 + 5 m = 3.605551275 + 5 Combine like terms: 3.605551275 + 5 = 8.605551275 m = 8.605551275 Simplifying m = 8.605551275

Subproblem 2

m + -5 = -3.605551275 Simplifying m + -5 = -3.605551275 Reorder the terms: -5 + m = -3.605551275 Solving -5 + m = -3.605551275 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + m = -3.605551275 + 5 Combine like terms: -5 + 5 = 0 0 + m = -3.605551275 + 5 m = -3.605551275 + 5 Combine like terms: -3.605551275 + 5 = 1.394448725 m = 1.394448725 Simplifying m = 1.394448725

Solution

The solution to the problem is based on the solutions from the subproblems. m = {8.605551275, 1.394448725}

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