9m^2=4+7m

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Solution for 9m^2=4+7m equation:


Simplifying
9m2 = 4 + 7m

Solving
9m2 = 4 + 7m

Solving for variable 'm'.

Reorder the terms:
-4 + -7m + 9m2 = 4 + 7m + -4 + -7m

Reorder the terms:
-4 + -7m + 9m2 = 4 + -4 + 7m + -7m

Combine like terms: 4 + -4 = 0
-4 + -7m + 9m2 = 0 + 7m + -7m
-4 + -7m + 9m2 = 7m + -7m

Combine like terms: 7m + -7m = 0
-4 + -7m + 9m2 = 0

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

Divide each side by '9'.
-0.4444444444 + -0.7777777778m + m2 = 0

Move the constant term to the right:

Add '0.4444444444' to each side of the equation.
-0.4444444444 + -0.7777777778m + 0.4444444444 + m2 = 0 + 0.4444444444

Reorder the terms:
-0.4444444444 + 0.4444444444 + -0.7777777778m + m2 = 0 + 0.4444444444

Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000
0.0000000000 + -0.7777777778m + m2 = 0 + 0.4444444444
-0.7777777778m + m2 = 0 + 0.4444444444

Combine like terms: 0 + 0.4444444444 = 0.4444444444
-0.7777777778m + m2 = 0.4444444444

The m term is -0.7777777778m.  Take half its coefficient (-0.3888888889).
Square it (0.1512345679) and add it to both sides.

Add '0.1512345679' to each side of the equation.
-0.7777777778m + 0.1512345679 + m2 = 0.4444444444 + 0.1512345679

Reorder the terms:
0.1512345679 + -0.7777777778m + m2 = 0.4444444444 + 0.1512345679

Combine like terms: 0.4444444444 + 0.1512345679 = 0.5956790123
0.1512345679 + -0.7777777778m + m2 = 0.5956790123

Factor a perfect square on the left side:
(m + -0.3888888889)(m + -0.3888888889) = 0.5956790123

Calculate the square root of the right side: 0.771802444

Break this problem into two subproblems by setting 
(m + -0.3888888889) equal to 0.771802444 and -0.771802444.

Subproblem 1

m + -0.3888888889 = 0.771802444 Simplifying m + -0.3888888889 = 0.771802444 Reorder the terms: -0.3888888889 + m = 0.771802444 Solving -0.3888888889 + m = 0.771802444 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.3888888889' to each side of the equation. -0.3888888889 + 0.3888888889 + m = 0.771802444 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + m = 0.771802444 + 0.3888888889 m = 0.771802444 + 0.3888888889 Combine like terms: 0.771802444 + 0.3888888889 = 1.1606913329 m = 1.1606913329 Simplifying m = 1.1606913329

Subproblem 2

m + -0.3888888889 = -0.771802444 Simplifying m + -0.3888888889 = -0.771802444 Reorder the terms: -0.3888888889 + m = -0.771802444 Solving -0.3888888889 + m = -0.771802444 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.3888888889' to each side of the equation. -0.3888888889 + 0.3888888889 + m = -0.771802444 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + m = -0.771802444 + 0.3888888889 m = -0.771802444 + 0.3888888889 Combine like terms: -0.771802444 + 0.3888888889 = -0.3829135551 m = -0.3829135551 Simplifying m = -0.3829135551

Solution

The solution to the problem is based on the solutions from the subproblems. m = {1.1606913329, -0.3829135551}

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