2r^2+8r+7=0

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Solution for 2r^2+8r+7=0 equation:


Simplifying
2r2 + 8r + 7 = 0

Reorder the terms:
7 + 8r + 2r2 = 0

Solving
7 + 8r + 2r2 = 0

Solving for variable 'r'.

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

Divide each side by '2'.
3.5 + 4r + r2 = 0

Move the constant term to the right:

Add '-3.5' to each side of the equation.
3.5 + 4r + -3.5 + r2 = 0 + -3.5

Reorder the terms:
3.5 + -3.5 + 4r + r2 = 0 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + 4r + r2 = 0 + -3.5
4r + r2 = 0 + -3.5

Combine like terms: 0 + -3.5 = -3.5
4r + r2 = -3.5

The r term is 4r.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4r + 4 + r2 = -3.5 + 4

Reorder the terms:
4 + 4r + r2 = -3.5 + 4

Combine like terms: -3.5 + 4 = 0.5
4 + 4r + r2 = 0.5

Factor a perfect square on the left side:
(r + 2)(r + 2) = 0.5

Calculate the square root of the right side: 0.707106781

Break this problem into two subproblems by setting 
(r + 2) equal to 0.707106781 and -0.707106781.

Subproblem 1

r + 2 = 0.707106781 Simplifying r + 2 = 0.707106781 Reorder the terms: 2 + r = 0.707106781 Solving 2 + r = 0.707106781 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + r = 0.707106781 + -2 Combine like terms: 2 + -2 = 0 0 + r = 0.707106781 + -2 r = 0.707106781 + -2 Combine like terms: 0.707106781 + -2 = -1.292893219 r = -1.292893219 Simplifying r = -1.292893219

Subproblem 2

r + 2 = -0.707106781 Simplifying r + 2 = -0.707106781 Reorder the terms: 2 + r = -0.707106781 Solving 2 + r = -0.707106781 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + r = -0.707106781 + -2 Combine like terms: 2 + -2 = 0 0 + r = -0.707106781 + -2 r = -0.707106781 + -2 Combine like terms: -0.707106781 + -2 = -2.707106781 r = -2.707106781 Simplifying r = -2.707106781

Solution

The solution to the problem is based on the solutions from the subproblems. r = {-1.292893219, -2.707106781}

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