9m^2-11m=15

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Solution for 9m^2-11m=15 equation:


Simplifying
9m2 + -11m = 15

Reorder the terms:
-11m + 9m2 = 15

Solving
-11m + 9m2 = 15

Solving for variable 'm'.

Reorder the terms:
-15 + -11m + 9m2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + -11m + 9m2 = 0

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

Divide each side by '9'.
-1.666666667 + -1.222222222m + m2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + -1.222222222m + 1.666666667 + m2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + -1.222222222m + m2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + -1.222222222m + m2 = 0 + 1.666666667
-1.222222222m + m2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
-1.222222222m + m2 = 1.666666667

The m term is -1.222222222m.  Take half its coefficient (-0.611111111).
Square it (0.3734567900) and add it to both sides.

Add '0.3734567900' to each side of the equation.
-1.222222222m + 0.3734567900 + m2 = 1.666666667 + 0.3734567900

Reorder the terms:
0.3734567900 + -1.222222222m + m2 = 1.666666667 + 0.3734567900

Combine like terms: 1.666666667 + 0.3734567900 = 2.040123457
0.3734567900 + -1.222222222m + m2 = 2.040123457

Factor a perfect square on the left side:
(m + -0.611111111)(m + -0.611111111) = 2.040123457

Calculate the square root of the right side: 1.428328904

Break this problem into two subproblems by setting 
(m + -0.611111111) equal to 1.428328904 and -1.428328904.

Subproblem 1

m + -0.611111111 = 1.428328904 Simplifying m + -0.611111111 = 1.428328904 Reorder the terms: -0.611111111 + m = 1.428328904 Solving -0.611111111 + m = 1.428328904 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.611111111' to each side of the equation. -0.611111111 + 0.611111111 + m = 1.428328904 + 0.611111111 Combine like terms: -0.611111111 + 0.611111111 = 0.000000000 0.000000000 + m = 1.428328904 + 0.611111111 m = 1.428328904 + 0.611111111 Combine like terms: 1.428328904 + 0.611111111 = 2.039440015 m = 2.039440015 Simplifying m = 2.039440015

Subproblem 2

m + -0.611111111 = -1.428328904 Simplifying m + -0.611111111 = -1.428328904 Reorder the terms: -0.611111111 + m = -1.428328904 Solving -0.611111111 + m = -1.428328904 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.611111111' to each side of the equation. -0.611111111 + 0.611111111 + m = -1.428328904 + 0.611111111 Combine like terms: -0.611111111 + 0.611111111 = 0.000000000 0.000000000 + m = -1.428328904 + 0.611111111 m = -1.428328904 + 0.611111111 Combine like terms: -1.428328904 + 0.611111111 = -0.817217793 m = -0.817217793 Simplifying m = -0.817217793

Solution

The solution to the problem is based on the solutions from the subproblems. m = {2.039440015, -0.817217793}

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