r^2+5=-(10r-r^2)

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Solution for r^2+5=-(10r-r^2) equation:


Simplifying
r2 + 5 = -1(10r + -1r2)

Reorder the terms:
5 + r2 = -1(10r + -1r2)
5 + r2 = (10r * -1 + -1r2 * -1)
5 + r2 = (-10r + 1r2)

Solving
5 + r2 = -10r + 1r2

Solving for variable 'r'.

Reorder the terms:
5 + 10r + r2 + -1r2 = -10r + 1r2 + 10r + -1r2

Combine like terms: r2 + -1r2 = 0
5 + 10r + 0 = -10r + 1r2 + 10r + -1r2
5 + 10r = -10r + 1r2 + 10r + -1r2

Reorder the terms:
5 + 10r = -10r + 10r + 1r2 + -1r2

Combine like terms: -10r + 10r = 0
5 + 10r = 0 + 1r2 + -1r2
5 + 10r = 1r2 + -1r2

Combine like terms: 1r2 + -1r2 = 0
5 + 10r = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(1 + 2r) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(1 + 2r)' equal to zero and attempt to solve: Simplifying 1 + 2r = 0 Solving 1 + 2r = 0 Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2r = 0 + -1 2r = 0 + -1 Combine like terms: 0 + -1 = -1 2r = -1 Divide each side by '2'. r = -0.5 Simplifying r = -0.5

Solution

r = {-0.5}

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