4m^2-17m-22=0

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Solution for 4m^2-17m-22=0 equation:


Simplifying
4m2 + -17m + -22 = 0

Reorder the terms:
-22 + -17m + 4m2 = 0

Solving
-22 + -17m + 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'.
-5.5 + -4.25m + m2 = 0

Move the constant term to the right:

Add '5.5' to each side of the equation.
-5.5 + -4.25m + 5.5 + m2 = 0 + 5.5

Reorder the terms:
-5.5 + 5.5 + -4.25m + m2 = 0 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + -4.25m + m2 = 0 + 5.5
-4.25m + m2 = 0 + 5.5

Combine like terms: 0 + 5.5 = 5.5
-4.25m + m2 = 5.5

The m term is -4.25m.  Take half its coefficient (-2.125).
Square it (4.515625) and add it to both sides.

Add '4.515625' to each side of the equation.
-4.25m + 4.515625 + m2 = 5.5 + 4.515625

Reorder the terms:
4.515625 + -4.25m + m2 = 5.5 + 4.515625

Combine like terms: 5.5 + 4.515625 = 10.015625
4.515625 + -4.25m + m2 = 10.015625

Factor a perfect square on the left side:
(m + -2.125)(m + -2.125) = 10.015625

Calculate the square root of the right side: 3.164747225

Break this problem into two subproblems by setting 
(m + -2.125) equal to 3.164747225 and -3.164747225.

Subproblem 1

m + -2.125 = 3.164747225 Simplifying m + -2.125 = 3.164747225 Reorder the terms: -2.125 + m = 3.164747225 Solving -2.125 + m = 3.164747225 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + m = 3.164747225 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + m = 3.164747225 + 2.125 m = 3.164747225 + 2.125 Combine like terms: 3.164747225 + 2.125 = 5.289747225 m = 5.289747225 Simplifying m = 5.289747225

Subproblem 2

m + -2.125 = -3.164747225 Simplifying m + -2.125 = -3.164747225 Reorder the terms: -2.125 + m = -3.164747225 Solving -2.125 + m = -3.164747225 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + m = -3.164747225 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + m = -3.164747225 + 2.125 m = -3.164747225 + 2.125 Combine like terms: -3.164747225 + 2.125 = -1.039747225 m = -1.039747225 Simplifying m = -1.039747225

Solution

The solution to the problem is based on the solutions from the subproblems. m = {5.289747225, -1.039747225}

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