4m^2+9m=23

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Solution for 4m^2+9m=23 equation:


Simplifying
4m2 + 9m = 23

Reorder the terms:
9m + 4m2 = 23

Solving
9m + 4m2 = 23

Solving for variable 'm'.

Reorder the terms:
-23 + 9m + 4m2 = 23 + -23

Combine like terms: 23 + -23 = 0
-23 + 9m + 4m2 = 0

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

Divide each side by '4'.
-5.75 + 2.25m + m2 = 0

Move the constant term to the right:

Add '5.75' to each side of the equation.
-5.75 + 2.25m + 5.75 + m2 = 0 + 5.75

Reorder the terms:
-5.75 + 5.75 + 2.25m + m2 = 0 + 5.75

Combine like terms: -5.75 + 5.75 = 0.00
0.00 + 2.25m + m2 = 0 + 5.75
2.25m + m2 = 0 + 5.75

Combine like terms: 0 + 5.75 = 5.75
2.25m + m2 = 5.75

The m term is 2.25m.  Take half its coefficient (1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
2.25m + 1.265625 + m2 = 5.75 + 1.265625

Reorder the terms:
1.265625 + 2.25m + m2 = 5.75 + 1.265625

Combine like terms: 5.75 + 1.265625 = 7.015625
1.265625 + 2.25m + m2 = 7.015625

Factor a perfect square on the left side:
(m + 1.125)(m + 1.125) = 7.015625

Calculate the square root of the right side: 2.648702513

Break this problem into two subproblems by setting 
(m + 1.125) equal to 2.648702513 and -2.648702513.

Subproblem 1

m + 1.125 = 2.648702513 Simplifying m + 1.125 = 2.648702513 Reorder the terms: 1.125 + m = 2.648702513 Solving 1.125 + m = 2.648702513 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + m = 2.648702513 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + m = 2.648702513 + -1.125 m = 2.648702513 + -1.125 Combine like terms: 2.648702513 + -1.125 = 1.523702513 m = 1.523702513 Simplifying m = 1.523702513

Subproblem 2

m + 1.125 = -2.648702513 Simplifying m + 1.125 = -2.648702513 Reorder the terms: 1.125 + m = -2.648702513 Solving 1.125 + m = -2.648702513 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + m = -2.648702513 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + m = -2.648702513 + -1.125 m = -2.648702513 + -1.125 Combine like terms: -2.648702513 + -1.125 = -3.773702513 m = -3.773702513 Simplifying m = -3.773702513

Solution

The solution to the problem is based on the solutions from the subproblems. m = {1.523702513, -3.773702513}

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