7m+25=2+2m^2

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Solution for 7m+25=2+2m^2 equation:


Simplifying
7m + 25 = 2 + 2m2

Reorder the terms:
25 + 7m = 2 + 2m2

Solving
25 + 7m = 2 + 2m2

Solving for variable 'm'.

Reorder the terms:
25 + -2 + 7m + -2m2 = 2 + 2m2 + -2 + -2m2

Combine like terms: 25 + -2 = 23
23 + 7m + -2m2 = 2 + 2m2 + -2 + -2m2

Reorder the terms:
23 + 7m + -2m2 = 2 + -2 + 2m2 + -2m2

Combine like terms: 2 + -2 = 0
23 + 7m + -2m2 = 0 + 2m2 + -2m2
23 + 7m + -2m2 = 2m2 + -2m2

Combine like terms: 2m2 + -2m2 = 0
23 + 7m + -2m2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-11.5 + -3.5m + m2 = 0

Move the constant term to the right:

Add '11.5' to each side of the equation.
-11.5 + -3.5m + 11.5 + m2 = 0 + 11.5

Reorder the terms:
-11.5 + 11.5 + -3.5m + m2 = 0 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + -3.5m + m2 = 0 + 11.5
-3.5m + m2 = 0 + 11.5

Combine like terms: 0 + 11.5 = 11.5
-3.5m + m2 = 11.5

The m term is -3.5m.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5m + 3.0625 + m2 = 11.5 + 3.0625

Reorder the terms:
3.0625 + -3.5m + m2 = 11.5 + 3.0625

Combine like terms: 11.5 + 3.0625 = 14.5625
3.0625 + -3.5m + m2 = 14.5625

Factor a perfect square on the left side:
(m + -1.75)(m + -1.75) = 14.5625

Calculate the square root of the right side: 3.816084381

Break this problem into two subproblems by setting 
(m + -1.75) equal to 3.816084381 and -3.816084381.

Subproblem 1

m + -1.75 = 3.816084381 Simplifying m + -1.75 = 3.816084381 Reorder the terms: -1.75 + m = 3.816084381 Solving -1.75 + m = 3.816084381 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + m = 3.816084381 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + m = 3.816084381 + 1.75 m = 3.816084381 + 1.75 Combine like terms: 3.816084381 + 1.75 = 5.566084381 m = 5.566084381 Simplifying m = 5.566084381

Subproblem 2

m + -1.75 = -3.816084381 Simplifying m + -1.75 = -3.816084381 Reorder the terms: -1.75 + m = -3.816084381 Solving -1.75 + m = -3.816084381 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + m = -3.816084381 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + m = -3.816084381 + 1.75 m = -3.816084381 + 1.75 Combine like terms: -3.816084381 + 1.75 = -2.066084381 m = -2.066084381 Simplifying m = -2.066084381

Solution

The solution to the problem is based on the solutions from the subproblems. m = {5.566084381, -2.066084381}

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