4m^2+2m-11=0

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Solution for 4m^2+2m-11=0 equation:


Simplifying
4m2 + 2m + -11 = 0

Reorder the terms:
-11 + 2m + 4m2 = 0

Solving
-11 + 2m + 4m2 = 0

Solving for variable 'm'.

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

Divide each side by '4'.
-2.75 + 0.5m + m2 = 0

Move the constant term to the right:

Add '2.75' to each side of the equation.
-2.75 + 0.5m + 2.75 + m2 = 0 + 2.75

Reorder the terms:
-2.75 + 2.75 + 0.5m + m2 = 0 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + 0.5m + m2 = 0 + 2.75
0.5m + m2 = 0 + 2.75

Combine like terms: 0 + 2.75 = 2.75
0.5m + m2 = 2.75

The m term is 0.5m.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5m + 0.0625 + m2 = 2.75 + 0.0625

Reorder the terms:
0.0625 + 0.5m + m2 = 2.75 + 0.0625

Combine like terms: 2.75 + 0.0625 = 2.8125
0.0625 + 0.5m + m2 = 2.8125

Factor a perfect square on the left side:
(m + 0.25)(m + 0.25) = 2.8125

Calculate the square root of the right side: 1.677050983

Break this problem into two subproblems by setting 
(m + 0.25) equal to 1.677050983 and -1.677050983.

Subproblem 1

m + 0.25 = 1.677050983 Simplifying m + 0.25 = 1.677050983 Reorder the terms: 0.25 + m = 1.677050983 Solving 0.25 + m = 1.677050983 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + m = 1.677050983 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + m = 1.677050983 + -0.25 m = 1.677050983 + -0.25 Combine like terms: 1.677050983 + -0.25 = 1.427050983 m = 1.427050983 Simplifying m = 1.427050983

Subproblem 2

m + 0.25 = -1.677050983 Simplifying m + 0.25 = -1.677050983 Reorder the terms: 0.25 + m = -1.677050983 Solving 0.25 + m = -1.677050983 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + m = -1.677050983 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + m = -1.677050983 + -0.25 m = -1.677050983 + -0.25 Combine like terms: -1.677050983 + -0.25 = -1.927050983 m = -1.927050983 Simplifying m = -1.927050983

Solution

The solution to the problem is based on the solutions from the subproblems. m = {1.427050983, -1.927050983}

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