m^2=14(3-m)

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Solution for m^2=14(3-m) equation:


Simplifying
m2 = 14(3 + -1m)
m2 = (3 * 14 + -1m * 14)
m2 = (42 + -14m)

Solving
m2 = 42 + -14m

Solving for variable 'm'.

Reorder the terms:
-42 + 14m + m2 = 42 + -14m + -42 + 14m

Reorder the terms:
-42 + 14m + m2 = 42 + -42 + -14m + 14m

Combine like terms: 42 + -42 = 0
-42 + 14m + m2 = 0 + -14m + 14m
-42 + 14m + m2 = -14m + 14m

Combine like terms: -14m + 14m = 0
-42 + 14m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '42' to each side of the equation.
-42 + 14m + 42 + m2 = 0 + 42

Reorder the terms:
-42 + 42 + 14m + m2 = 0 + 42

Combine like terms: -42 + 42 = 0
0 + 14m + m2 = 0 + 42
14m + m2 = 0 + 42

Combine like terms: 0 + 42 = 42
14m + m2 = 42

The m term is 14m.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14m + 49 + m2 = 42 + 49

Reorder the terms:
49 + 14m + m2 = 42 + 49

Combine like terms: 42 + 49 = 91
49 + 14m + m2 = 91

Factor a perfect square on the left side:
(m + 7)(m + 7) = 91

Calculate the square root of the right side: 9.539392014

Break this problem into two subproblems by setting 
(m + 7) equal to 9.539392014 and -9.539392014.

Subproblem 1

m + 7 = 9.539392014 Simplifying m + 7 = 9.539392014 Reorder the terms: 7 + m = 9.539392014 Solving 7 + m = 9.539392014 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + m = 9.539392014 + -7 Combine like terms: 7 + -7 = 0 0 + m = 9.539392014 + -7 m = 9.539392014 + -7 Combine like terms: 9.539392014 + -7 = 2.539392014 m = 2.539392014 Simplifying m = 2.539392014

Subproblem 2

m + 7 = -9.539392014 Simplifying m + 7 = -9.539392014 Reorder the terms: 7 + m = -9.539392014 Solving 7 + m = -9.539392014 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + m = -9.539392014 + -7 Combine like terms: 7 + -7 = 0 0 + m = -9.539392014 + -7 m = -9.539392014 + -7 Combine like terms: -9.539392014 + -7 = -16.539392014 m = -16.539392014 Simplifying m = -16.539392014

Solution

The solution to the problem is based on the solutions from the subproblems. m = {2.539392014, -16.539392014}

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