-2m^2+11m-10=0

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Solution for -2m^2+11m-10=0 equation:


Simplifying
-2m2 + 11m + -10 = 0

Reorder the terms:
-10 + 11m + -2m2 = 0

Solving
-10 + 11m + -2m2 = 0

Solving for variable 'm'.

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
5 + -5.5m + m2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -5.5m + -5 + m2 = 0 + -5

Reorder the terms:
5 + -5 + -5.5m + m2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -5.5m + m2 = 0 + -5
-5.5m + m2 = 0 + -5

Combine like terms: 0 + -5 = -5
-5.5m + m2 = -5

The m term is -5.5m.  Take half its coefficient (-2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
-5.5m + 7.5625 + m2 = -5 + 7.5625

Reorder the terms:
7.5625 + -5.5m + m2 = -5 + 7.5625

Combine like terms: -5 + 7.5625 = 2.5625
7.5625 + -5.5m + m2 = 2.5625

Factor a perfect square on the left side:
(m + -2.75)(m + -2.75) = 2.5625

Calculate the square root of the right side: 1.600781059

Break this problem into two subproblems by setting 
(m + -2.75) equal to 1.600781059 and -1.600781059.

Subproblem 1

m + -2.75 = 1.600781059 Simplifying m + -2.75 = 1.600781059 Reorder the terms: -2.75 + m = 1.600781059 Solving -2.75 + m = 1.600781059 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + m = 1.600781059 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + m = 1.600781059 + 2.75 m = 1.600781059 + 2.75 Combine like terms: 1.600781059 + 2.75 = 4.350781059 m = 4.350781059 Simplifying m = 4.350781059

Subproblem 2

m + -2.75 = -1.600781059 Simplifying m + -2.75 = -1.600781059 Reorder the terms: -2.75 + m = -1.600781059 Solving -2.75 + m = -1.600781059 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + m = -1.600781059 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + m = -1.600781059 + 2.75 m = -1.600781059 + 2.75 Combine like terms: -1.600781059 + 2.75 = 1.149218941 m = 1.149218941 Simplifying m = 1.149218941

Solution

The solution to the problem is based on the solutions from the subproblems. m = {4.350781059, 1.149218941}

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