r^2+28r=-23

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Solution for r^2+28r=-23 equation:


Simplifying
r2 + 28r = -23

Reorder the terms:
28r + r2 = -23

Solving
28r + r2 = -23

Solving for variable 'r'.

Reorder the terms:
23 + 28r + r2 = -23 + 23

Combine like terms: -23 + 23 = 0
23 + 28r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-23' to each side of the equation.
23 + 28r + -23 + r2 = 0 + -23

Reorder the terms:
23 + -23 + 28r + r2 = 0 + -23

Combine like terms: 23 + -23 = 0
0 + 28r + r2 = 0 + -23
28r + r2 = 0 + -23

Combine like terms: 0 + -23 = -23
28r + r2 = -23

The r term is 28r.  Take half its coefficient (14).
Square it (196) and add it to both sides.

Add '196' to each side of the equation.
28r + 196 + r2 = -23 + 196

Reorder the terms:
196 + 28r + r2 = -23 + 196

Combine like terms: -23 + 196 = 173
196 + 28r + r2 = 173

Factor a perfect square on the left side:
(r + 14)(r + 14) = 173

Calculate the square root of the right side: 13.152946438

Break this problem into two subproblems by setting 
(r + 14) equal to 13.152946438 and -13.152946438.

Subproblem 1

r + 14 = 13.152946438 Simplifying r + 14 = 13.152946438 Reorder the terms: 14 + r = 13.152946438 Solving 14 + r = 13.152946438 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + r = 13.152946438 + -14 Combine like terms: 14 + -14 = 0 0 + r = 13.152946438 + -14 r = 13.152946438 + -14 Combine like terms: 13.152946438 + -14 = -0.847053562 r = -0.847053562 Simplifying r = -0.847053562

Subproblem 2

r + 14 = -13.152946438 Simplifying r + 14 = -13.152946438 Reorder the terms: 14 + r = -13.152946438 Solving 14 + r = -13.152946438 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + r = -13.152946438 + -14 Combine like terms: 14 + -14 = 0 0 + r = -13.152946438 + -14 r = -13.152946438 + -14 Combine like terms: -13.152946438 + -14 = -27.152946438 r = -27.152946438 Simplifying r = -27.152946438

Solution

The solution to the problem is based on the solutions from the subproblems. r = {-0.847053562, -27.152946438}

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