m^2-10m+18=0

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Solution for m^2-10m+18=0 equation:


Simplifying
m2 + -10m + 18 = 0

Reorder the terms:
18 + -10m + m2 = 0

Solving
18 + -10m + m2 = 0

Solving for variable 'm'.

Begin completing the square.

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + -10m + -18 + m2 = 0 + -18

Reorder the terms:
18 + -18 + -10m + m2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -10m + m2 = 0 + -18
-10m + m2 = 0 + -18

Combine like terms: 0 + -18 = -18
-10m + m2 = -18

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 = -18 + 25

Reorder the terms:
25 + -10m + m2 = -18 + 25

Combine like terms: -18 + 25 = 7
25 + -10m + m2 = 7

Factor a perfect square on the left side:
(m + -5)(m + -5) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(m + -5) equal to 2.645751311 and -2.645751311.

Subproblem 1

m + -5 = 2.645751311 Simplifying m + -5 = 2.645751311 Reorder the terms: -5 + m = 2.645751311 Solving -5 + m = 2.645751311 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 = 2.645751311 + 5 Combine like terms: -5 + 5 = 0 0 + m = 2.645751311 + 5 m = 2.645751311 + 5 Combine like terms: 2.645751311 + 5 = 7.645751311 m = 7.645751311 Simplifying m = 7.645751311

Subproblem 2

m + -5 = -2.645751311 Simplifying m + -5 = -2.645751311 Reorder the terms: -5 + m = -2.645751311 Solving -5 + m = -2.645751311 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 = -2.645751311 + 5 Combine like terms: -5 + 5 = 0 0 + m = -2.645751311 + 5 m = -2.645751311 + 5 Combine like terms: -2.645751311 + 5 = 2.354248689 m = 2.354248689 Simplifying m = 2.354248689

Solution

The solution to the problem is based on the solutions from the subproblems. m = {7.645751311, 2.354248689}

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