7r^2-28r-21=3

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Solution for 7r^2-28r-21=3 equation:


Simplifying
7r2 + -28r + -21 = 3

Reorder the terms:
-21 + -28r + 7r2 = 3

Solving
-21 + -28r + 7r2 = 3

Solving for variable 'r'.

Reorder the terms:
-21 + -3 + -28r + 7r2 = 3 + -3

Combine like terms: -21 + -3 = -24
-24 + -28r + 7r2 = 3 + -3

Combine like terms: 3 + -3 = 0
-24 + -28r + 7r2 = 0

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

Divide each side by '7'.
-3.428571429 + -4r + r2 = 0

Move the constant term to the right:

Add '3.428571429' to each side of the equation.
-3.428571429 + -4r + 3.428571429 + r2 = 0 + 3.428571429

Reorder the terms:
-3.428571429 + 3.428571429 + -4r + r2 = 0 + 3.428571429

Combine like terms: -3.428571429 + 3.428571429 = 0.000000000
0.000000000 + -4r + r2 = 0 + 3.428571429
-4r + r2 = 0 + 3.428571429

Combine like terms: 0 + 3.428571429 = 3.428571429
-4r + r2 = 3.428571429

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 = 3.428571429 + 4

Reorder the terms:
4 + -4r + r2 = 3.428571429 + 4

Combine like terms: 3.428571429 + 4 = 7.428571429
4 + -4r + r2 = 7.428571429

Factor a perfect square on the left side:
(r + -2)(r + -2) = 7.428571429

Calculate the square root of the right side: 2.725540576

Break this problem into two subproblems by setting 
(r + -2) equal to 2.725540576 and -2.725540576.

Subproblem 1

r + -2 = 2.725540576 Simplifying r + -2 = 2.725540576 Reorder the terms: -2 + r = 2.725540576 Solving -2 + r = 2.725540576 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 = 2.725540576 + 2 Combine like terms: -2 + 2 = 0 0 + r = 2.725540576 + 2 r = 2.725540576 + 2 Combine like terms: 2.725540576 + 2 = 4.725540576 r = 4.725540576 Simplifying r = 4.725540576

Subproblem 2

r + -2 = -2.725540576 Simplifying r + -2 = -2.725540576 Reorder the terms: -2 + r = -2.725540576 Solving -2 + r = -2.725540576 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 = -2.725540576 + 2 Combine like terms: -2 + 2 = 0 0 + r = -2.725540576 + 2 r = -2.725540576 + 2 Combine like terms: -2.725540576 + 2 = -0.725540576 r = -0.725540576 Simplifying r = -0.725540576

Solution

The solution to the problem is based on the solutions from the subproblems. r = {4.725540576, -0.725540576}

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