m^2-28m=-9

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Solution for m^2-28m=-9 equation:


Simplifying
m2 + -28m = -9

Reorder the terms:
-28m + m2 = -9

Solving
-28m + m2 = -9

Solving for variable 'm'.

Reorder the terms:
9 + -28m + m2 = -9 + 9

Combine like terms: -9 + 9 = 0
9 + -28m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + -28m + -9 + m2 = 0 + -9

Reorder the terms:
9 + -9 + -28m + m2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -28m + m2 = 0 + -9
-28m + m2 = 0 + -9

Combine like terms: 0 + -9 = -9
-28m + m2 = -9

The m term is -28m.  Take half its coefficient (-14).
Square it (196) and add it to both sides.

Add '196' to each side of the equation.
-28m + 196 + m2 = -9 + 196

Reorder the terms:
196 + -28m + m2 = -9 + 196

Combine like terms: -9 + 196 = 187
196 + -28m + m2 = 187

Factor a perfect square on the left side:
(m + -14)(m + -14) = 187

Calculate the square root of the right side: 13.674794331

Break this problem into two subproblems by setting 
(m + -14) equal to 13.674794331 and -13.674794331.

Subproblem 1

m + -14 = 13.674794331 Simplifying m + -14 = 13.674794331 Reorder the terms: -14 + m = 13.674794331 Solving -14 + m = 13.674794331 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + m = 13.674794331 + 14 Combine like terms: -14 + 14 = 0 0 + m = 13.674794331 + 14 m = 13.674794331 + 14 Combine like terms: 13.674794331 + 14 = 27.674794331 m = 27.674794331 Simplifying m = 27.674794331

Subproblem 2

m + -14 = -13.674794331 Simplifying m + -14 = -13.674794331 Reorder the terms: -14 + m = -13.674794331 Solving -14 + m = -13.674794331 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + m = -13.674794331 + 14 Combine like terms: -14 + 14 = 0 0 + m = -13.674794331 + 14 m = -13.674794331 + 14 Combine like terms: -13.674794331 + 14 = 0.325205669 m = 0.325205669 Simplifying m = 0.325205669

Solution

The solution to the problem is based on the solutions from the subproblems. m = {27.674794331, 0.325205669}

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