Solve for x
x=4
x=-4
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3x^{2}-35-45=-2x^{2}
Subtract 45 from both sides.
3x^{2}-80=-2x^{2}
Subtract 45 from -35 to get -80.
3x^{2}-80+2x^{2}=0
Add 2x^{2} to both sides.
5x^{2}-80=0
Combine 3x^{2} and 2x^{2} to get 5x^{2}.
x^{2}-16=0
Divide both sides by 5.
\left(x-4\right)\left(x+4\right)=0
Consider x^{2}-16. Rewrite x^{2}-16 as x^{2}-4^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).
x=4 x=-4
To find equation solutions, solve x-4=0 and x+4=0.
3x^{2}-35+2x^{2}=45
Add 2x^{2} to both sides.
5x^{2}-35=45
Combine 3x^{2} and 2x^{2} to get 5x^{2}.
5x^{2}=45+35
Add 35 to both sides.
5x^{2}=80
Add 45 and 35 to get 80.
x^{2}=\frac{80}{5}
Divide both sides by 5.
x^{2}=16
Divide 80 by 5 to get 16.
x=4 x=-4
Take the square root of both sides of the equation.
3x^{2}-35-45=-2x^{2}
Subtract 45 from both sides.
3x^{2}-80=-2x^{2}
Subtract 45 from -35 to get -80.
3x^{2}-80+2x^{2}=0
Add 2x^{2} to both sides.
5x^{2}-80=0
Combine 3x^{2} and 2x^{2} to get 5x^{2}.
x=\frac{0±\sqrt{0^{2}-4\times 5\left(-80\right)}}{2\times 5}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -80 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\times 5\left(-80\right)}}{2\times 5}
Square 0.
x=\frac{0±\sqrt{-20\left(-80\right)}}{2\times 5}
Multiply -4 times 5.
x=\frac{0±\sqrt{1600}}{2\times 5}
Multiply -20 times -80.
x=\frac{0±40}{2\times 5}
Take the square root of 1600.
x=\frac{0±40}{10}
Multiply 2 times 5.
x=4
Now solve the equation x=\frac{0±40}{10} when ± is plus. Divide 40 by 10.
x=-4
Now solve the equation x=\frac{0±40}{10} when ± is minus. Divide -40 by 10.
x=4 x=-4
The equation is now solved.
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