m^2-10m+10=14

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Solution for m^2-10m+10=14 equation:


Simplifying
m2 + -10m + 10 = 14

Reorder the terms:
10 + -10m + m2 = 14

Solving
10 + -10m + m2 = 14

Solving for variable 'm'.

Reorder the terms:
10 + -14 + -10m + m2 = 14 + -14

Combine like terms: 10 + -14 = -4
-4 + -10m + m2 = 14 + -14

Combine like terms: 14 + -14 = 0
-4 + -10m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -10m + 4 + m2 = 0 + 4

Reorder the terms:
-4 + 4 + -10m + m2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -10m + m2 = 0 + 4
-10m + m2 = 0 + 4

Combine like terms: 0 + 4 = 4
-10m + m2 = 4

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 = 4 + 25

Reorder the terms:
25 + -10m + m2 = 4 + 25

Combine like terms: 4 + 25 = 29
25 + -10m + m2 = 29

Factor a perfect square on the left side:
(m + -5)(m + -5) = 29

Calculate the square root of the right side: 5.385164807

Break this problem into two subproblems by setting 
(m + -5) equal to 5.385164807 and -5.385164807.

Subproblem 1

m + -5 = 5.385164807 Simplifying m + -5 = 5.385164807 Reorder the terms: -5 + m = 5.385164807 Solving -5 + m = 5.385164807 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 = 5.385164807 + 5 Combine like terms: -5 + 5 = 0 0 + m = 5.385164807 + 5 m = 5.385164807 + 5 Combine like terms: 5.385164807 + 5 = 10.385164807 m = 10.385164807 Simplifying m = 10.385164807

Subproblem 2

m + -5 = -5.385164807 Simplifying m + -5 = -5.385164807 Reorder the terms: -5 + m = -5.385164807 Solving -5 + m = -5.385164807 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 = -5.385164807 + 5 Combine like terms: -5 + 5 = 0 0 + m = -5.385164807 + 5 m = -5.385164807 + 5 Combine like terms: -5.385164807 + 5 = -0.385164807 m = -0.385164807 Simplifying m = -0.385164807

Solution

The solution to the problem is based on the solutions from the subproblems. m = {10.385164807, -0.385164807}

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