(r-4)(r+18)=4

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Solution for (r-4)(r+18)=4 equation:


Simplifying
(r + -4)(r + 18) = 4

Reorder the terms:
(-4 + r)(r + 18) = 4

Reorder the terms:
(-4 + r)(18 + r) = 4

Multiply (-4 + r) * (18 + r)
(-4(18 + r) + r(18 + r)) = 4
((18 * -4 + r * -4) + r(18 + r)) = 4
((-72 + -4r) + r(18 + r)) = 4
(-72 + -4r + (18 * r + r * r)) = 4
(-72 + -4r + (18r + r2)) = 4

Combine like terms: -4r + 18r = 14r
(-72 + 14r + r2) = 4

Solving
-72 + 14r + r2 = 4

Solving for variable 'r'.

Reorder the terms:
-72 + -4 + 14r + r2 = 4 + -4

Combine like terms: -72 + -4 = -76
-76 + 14r + r2 = 4 + -4

Combine like terms: 4 + -4 = 0
-76 + 14r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '76' to each side of the equation.
-76 + 14r + 76 + r2 = 0 + 76

Reorder the terms:
-76 + 76 + 14r + r2 = 0 + 76

Combine like terms: -76 + 76 = 0
0 + 14r + r2 = 0 + 76
14r + r2 = 0 + 76

Combine like terms: 0 + 76 = 76
14r + r2 = 76

The r term is 14r.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14r + 49 + r2 = 76 + 49

Reorder the terms:
49 + 14r + r2 = 76 + 49

Combine like terms: 76 + 49 = 125
49 + 14r + r2 = 125

Factor a perfect square on the left side:
(r + 7)(r + 7) = 125

Calculate the square root of the right side: 11.180339887

Break this problem into two subproblems by setting 
(r + 7) equal to 11.180339887 and -11.180339887.

Subproblem 1

r + 7 = 11.180339887 Simplifying r + 7 = 11.180339887 Reorder the terms: 7 + r = 11.180339887 Solving 7 + r = 11.180339887 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + r = 11.180339887 + -7 Combine like terms: 7 + -7 = 0 0 + r = 11.180339887 + -7 r = 11.180339887 + -7 Combine like terms: 11.180339887 + -7 = 4.180339887 r = 4.180339887 Simplifying r = 4.180339887

Subproblem 2

r + 7 = -11.180339887 Simplifying r + 7 = -11.180339887 Reorder the terms: 7 + r = -11.180339887 Solving 7 + r = -11.180339887 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + r = -11.180339887 + -7 Combine like terms: 7 + -7 = 0 0 + r = -11.180339887 + -7 r = -11.180339887 + -7 Combine like terms: -11.180339887 + -7 = -18.180339887 r = -18.180339887 Simplifying r = -18.180339887

Solution

The solution to the problem is based on the solutions from the subproblems. r = {4.180339887, -18.180339887}

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