2r^2-6r-7=0

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Solution for 2r^2-6r-7=0 equation:


Simplifying
2r2 + -6r + -7 = 0

Reorder the terms:
-7 + -6r + 2r2 = 0

Solving
-7 + -6r + 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 + -3r + r2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + -3r + 3.5 + r2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + -3r + r2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + -3r + r2 = 0 + 3.5
-3r + r2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
-3r + r2 = 3.5

The r term is -3r.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3r + 2.25 + r2 = 3.5 + 2.25

Reorder the terms:
2.25 + -3r + r2 = 3.5 + 2.25

Combine like terms: 3.5 + 2.25 = 5.75
2.25 + -3r + r2 = 5.75

Factor a perfect square on the left side:
(r + -1.5)(r + -1.5) = 5.75

Calculate the square root of the right side: 2.397915762

Break this problem into two subproblems by setting 
(r + -1.5) equal to 2.397915762 and -2.397915762.

Subproblem 1

r + -1.5 = 2.397915762 Simplifying r + -1.5 = 2.397915762 Reorder the terms: -1.5 + r = 2.397915762 Solving -1.5 + r = 2.397915762 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + r = 2.397915762 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + r = 2.397915762 + 1.5 r = 2.397915762 + 1.5 Combine like terms: 2.397915762 + 1.5 = 3.897915762 r = 3.897915762 Simplifying r = 3.897915762

Subproblem 2

r + -1.5 = -2.397915762 Simplifying r + -1.5 = -2.397915762 Reorder the terms: -1.5 + r = -2.397915762 Solving -1.5 + r = -2.397915762 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + r = -2.397915762 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + r = -2.397915762 + 1.5 r = -2.397915762 + 1.5 Combine like terms: -2.397915762 + 1.5 = -0.897915762 r = -0.897915762 Simplifying r = -0.897915762

Solution

The solution to the problem is based on the solutions from the subproblems. r = {3.897915762, -0.897915762}

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