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Simplifying
(4r + 7s)(4r + -7s) = 0
Multiply (4r + 7s) * (4r + -7s)
(4r * (4r + -7s) + 7s * (4r + -7s)) = 0
((4r * 4r + -7s * 4r) + 7s * (4r + -7s)) = 0
Reorder the terms:
((-28rs + 16r2) + 7s * (4r + -7s)) = 0
((-28rs + 16r2) + 7s * (4r + -7s)) = 0
(-28rs + 16r2 + (4r * 7s + -7s * 7s)) = 0
(-28rs + 16r2 + (28rs + -49s2)) = 0
Reorder the terms:
(-28rs + 28rs + 16r2 + -49s2) = 0
Combine like terms: -28rs + 28rs = 0
(0 + 16r2 + -49s2) = 0
(16r2 + -49s2) = 0
Solving
16r2 + -49s2 = 0
Solving for variable 'r'.
Move all terms containing r to the left, all other terms to the right.
Add '49s2' to each side of the equation.
16r2 + -49s2 + 49s2 = 0 + 49s2
Combine like terms: -49s2 + 49s2 = 0
16r2 + 0 = 0 + 49s2
16r2 = 0 + 49s2
Remove the zero:
16r2 = 49s2
Divide each side by '16'.
r2 = 3.0625s2
Simplifying
r2 = 3.0625s2
Take the square root of each side:
r = {-1.75s, 1.75s}
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