Solve for w (3w+2)w=35

Math
(3w+2)w=35
Simplify (3w+2)w.
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Apply the distributive property.
3w⋅w+2w=35
Multiply w by w by adding the exponents.
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Move w.
3(w⋅w)+2w=35
Multiply w by w.
3w2+2w=35
3w2+2w=35
3w2+2w=35
Move 35 to the left side of the equation by subtracting it from both sides.
3w2+2w-35=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=3, b=2, and c=-35 into the quadratic formula and solve for w.
-2±22-4⋅(3⋅-35)2⋅3
Simplify.
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Simplify the numerator.
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Raise 2 to the power of 2.
w=-2±4-4⋅(3⋅-35)2⋅3
Multiply 3 by -35.
w=-2±4-4⋅-1052⋅3
Multiply -4 by -105.
w=-2±4+4202⋅3
Add 4 and 420.
w=-2±4242⋅3
Rewrite 424 as 22⋅106.
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Factor 4 out of 424.
w=-2±4(106)2⋅3
Rewrite 4 as 22.
w=-2±22⋅1062⋅3
w=-2±22⋅1062⋅3
Pull terms out from under the radical.
w=-2±21062⋅3
w=-2±21062⋅3
Multiply 2 by 3.
w=-2±21066
Simplify -2±21066.
w=-1±1063
w=-1±1063
The final answer is the combination of both solutions.
w=-1-1063,-1+1063
The result can be shown in multiple forms.
Exact Form:
w=-1-1063,-1+1063
Decimal Form:
w=3.09854338…,-3.76521004…
Solve for w (3w+2)w=35

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