# Solve for w w-7^2=2w^2-6w+56 w-72=2w2-6w+56
Since w is on the right side of the equation, switch the sides so it is on the left side of the equation.
2w2-6w+56=w-72
Simplify each term.
Raise 7 to the power of 2.
2w2-6w+56=w-1⋅49
Multiply -1 by 49.
2w2-6w+56=w-49
2w2-6w+56=w-49
Move all terms containing w to the left side of the equation.
Subtract w from both sides of the equation.
2w2-6w+56-w=-49
Subtract w from -6w.
2w2-7w+56=-49
2w2-7w+56=-49
Move all terms to the left side of the equation and simplify.
Move 49 to the left side of the equation by adding it to both sides.
2w2-7w+56+49=0
Add 56 and 49.
2w2-7w+105=0
2w2-7w+105=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=2, b=-7, and c=105 into the quadratic formula and solve for w.
7±(-7)2-4⋅(2⋅105)2⋅2
Simplify.
Simplify the numerator.
Raise -7 to the power of 2.
w=7±49-4⋅(2⋅105)2⋅2
Multiply 2 by 105.
w=7±49-4⋅2102⋅2
Multiply -4 by 210.
w=7±49-8402⋅2
Subtract 840 from 49.
w=7±-7912⋅2
Rewrite -791 as -1(791).
w=7±-1⋅7912⋅2
Rewrite -1(791) as -1⋅791.
w=7±-1⋅7912⋅2
Rewrite -1 as i.
w=7±i7912⋅2
w=7±i7912⋅2
Multiply 2 by 2.
w=7±i7914
w=7±i7914
The final answer is the combination of both solutions.
w=7+i7914,7-i7914
Solve for w w-7^2=2w^2-6w+56

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