9m^2+8m=22

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Solution for 9m^2+8m=22 equation:


Simplifying
9m2 + 8m = 22

Reorder the terms:
8m + 9m2 = 22

Solving
8m + 9m2 = 22

Solving for variable 'm'.

Reorder the terms:
-22 + 8m + 9m2 = 22 + -22

Combine like terms: 22 + -22 = 0
-22 + 8m + 9m2 = 0

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

Divide each side by '9'.
-2.444444444 + 0.8888888889m + m2 = 0

Move the constant term to the right:

Add '2.444444444' to each side of the equation.
-2.444444444 + 0.8888888889m + 2.444444444 + m2 = 0 + 2.444444444

Reorder the terms:
-2.444444444 + 2.444444444 + 0.8888888889m + m2 = 0 + 2.444444444

Combine like terms: -2.444444444 + 2.444444444 = 0.000000000
0.000000000 + 0.8888888889m + m2 = 0 + 2.444444444
0.8888888889m + m2 = 0 + 2.444444444

Combine like terms: 0 + 2.444444444 = 2.444444444
0.8888888889m + m2 = 2.444444444

The m term is 0.8888888889m.  Take half its coefficient (0.4444444445).
Square it (0.1975308642) and add it to both sides.

Add '0.1975308642' to each side of the equation.
0.8888888889m + 0.1975308642 + m2 = 2.444444444 + 0.1975308642

Reorder the terms:
0.1975308642 + 0.8888888889m + m2 = 2.444444444 + 0.1975308642

Combine like terms: 2.444444444 + 0.1975308642 = 2.6419753082
0.1975308642 + 0.8888888889m + m2 = 2.6419753082

Factor a perfect square on the left side:
(m + 0.4444444445)(m + 0.4444444445) = 2.6419753082

Calculate the square root of the right side: 1.625415426

Break this problem into two subproblems by setting 
(m + 0.4444444445) equal to 1.625415426 and -1.625415426.

Subproblem 1

m + 0.4444444445 = 1.625415426 Simplifying m + 0.4444444445 = 1.625415426 Reorder the terms: 0.4444444445 + m = 1.625415426 Solving 0.4444444445 + m = 1.625415426 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + m = 1.625415426 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + m = 1.625415426 + -0.4444444445 m = 1.625415426 + -0.4444444445 Combine like terms: 1.625415426 + -0.4444444445 = 1.1809709815 m = 1.1809709815 Simplifying m = 1.1809709815

Subproblem 2

m + 0.4444444445 = -1.625415426 Simplifying m + 0.4444444445 = -1.625415426 Reorder the terms: 0.4444444445 + m = -1.625415426 Solving 0.4444444445 + m = -1.625415426 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + m = -1.625415426 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + m = -1.625415426 + -0.4444444445 m = -1.625415426 + -0.4444444445 Combine like terms: -1.625415426 + -0.4444444445 = -2.0698598705 m = -2.0698598705 Simplifying m = -2.0698598705

Solution

The solution to the problem is based on the solutions from the subproblems. m = {1.1809709815, -2.0698598705}

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