r^2+(r^2+4r+4)-74=0

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Solution for r^2+(r^2+4r+4)-74=0 equation:


Simplifying
r2 + (r2 + 4r + 4) + -74 = 0

Reorder the terms:
r2 + (4 + 4r + r2) + -74 = 0

Remove parenthesis around (4 + 4r + r2)
r2 + 4 + 4r + r2 + -74 = 0

Reorder the terms:
4 + -74 + 4r + r2 + r2 = 0

Combine like terms: 4 + -74 = -70
-70 + 4r + r2 + r2 = 0

Combine like terms: r2 + r2 = 2r2
-70 + 4r + 2r2 = 0

Solving
-70 + 4r + 2r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-35 + 2r + r2) = 0

Factor a trinomial.
2((-7 + -1r)(5 + -1r)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-7 + -1r)' equal to zero and attempt to solve: Simplifying -7 + -1r = 0 Solving -7 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1r = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1r = 0 + 7 -1r = 0 + 7 Combine like terms: 0 + 7 = 7 -1r = 7 Divide each side by '-1'. r = -7 Simplifying r = -7

Subproblem 2

Set the factor '(5 + -1r)' equal to zero and attempt to solve: Simplifying 5 + -1r = 0 Solving 5 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1r = 0 + -5 -1r = 0 + -5 Combine like terms: 0 + -5 = -5 -1r = -5 Divide each side by '-1'. r = 5 Simplifying r = 5

Solution

r = {-7, 5}

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