r^2+8r-90=5

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Solution for r^2+8r-90=5 equation:


Simplifying
r2 + 8r + -90 = 5

Reorder the terms:
-90 + 8r + r2 = 5

Solving
-90 + 8r + r2 = 5

Solving for variable 'r'.

Reorder the terms:
-90 + -5 + 8r + r2 = 5 + -5

Combine like terms: -90 + -5 = -95
-95 + 8r + r2 = 5 + -5

Combine like terms: 5 + -5 = 0
-95 + 8r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '95' to each side of the equation.
-95 + 8r + 95 + r2 = 0 + 95

Reorder the terms:
-95 + 95 + 8r + r2 = 0 + 95

Combine like terms: -95 + 95 = 0
0 + 8r + r2 = 0 + 95
8r + r2 = 0 + 95

Combine like terms: 0 + 95 = 95
8r + r2 = 95

The r term is 8r.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8r + 16 + r2 = 95 + 16

Reorder the terms:
16 + 8r + r2 = 95 + 16

Combine like terms: 95 + 16 = 111
16 + 8r + r2 = 111

Factor a perfect square on the left side:
(r + 4)(r + 4) = 111

Calculate the square root of the right side: 10.535653753

Break this problem into two subproblems by setting 
(r + 4) equal to 10.535653753 and -10.535653753.

Subproblem 1

r + 4 = 10.535653753 Simplifying r + 4 = 10.535653753 Reorder the terms: 4 + r = 10.535653753 Solving 4 + r = 10.535653753 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + r = 10.535653753 + -4 Combine like terms: 4 + -4 = 0 0 + r = 10.535653753 + -4 r = 10.535653753 + -4 Combine like terms: 10.535653753 + -4 = 6.535653753 r = 6.535653753 Simplifying r = 6.535653753

Subproblem 2

r + 4 = -10.535653753 Simplifying r + 4 = -10.535653753 Reorder the terms: 4 + r = -10.535653753 Solving 4 + r = -10.535653753 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + r = -10.535653753 + -4 Combine like terms: 4 + -4 = 0 0 + r = -10.535653753 + -4 r = -10.535653753 + -4 Combine like terms: -10.535653753 + -4 = -14.535653753 r = -14.535653753 Simplifying r = -14.535653753

Solution

The solution to the problem is based on the solutions from the subproblems. r = {6.535653753, -14.535653753}

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