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10w^{2}-w-5-3w+2
Combine 6w^{2} and 4w^{2} to get 10w^{2}.
10w^{2}-4w-5+2
Combine -w and -3w to get -4w.
10w^{2}-4w-3
Add -5 and 2 to get -3.
factor(10w^{2}-w-5-3w+2)
Combine 6w^{2} and 4w^{2} to get 10w^{2}.
factor(10w^{2}-4w-5+2)
Combine -w and -3w to get -4w.
factor(10w^{2}-4w-3)
Add -5 and 2 to get -3.
10w^{2}-4w-3=0
Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.
w=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\times 10\left(-3\right)}}{2\times 10}
All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.
w=\frac{-\left(-4\right)±\sqrt{16-4\times 10\left(-3\right)}}{2\times 10}
Square -4.
w=\frac{-\left(-4\right)±\sqrt{16-40\left(-3\right)}}{2\times 10}
Multiply -4 times 10.
w=\frac{-\left(-4\right)±\sqrt{16+120}}{2\times 10}
Multiply -40 times -3.
w=\frac{-\left(-4\right)±\sqrt{136}}{2\times 10}
Add 16 to 120.
w=\frac{-\left(-4\right)±2\sqrt{34}}{2\times 10}
Take the square root of 136.
w=\frac{4±2\sqrt{34}}{2\times 10}
The opposite of -4 is 4.
w=\frac{4±2\sqrt{34}}{20}
Multiply 2 times 10.
w=\frac{2\sqrt{34}+4}{20}
Now solve the equation w=\frac{4±2\sqrt{34}}{20} when ± is plus. Add 4 to 2\sqrt{34}\approx 11.66190379.
w=\frac{\sqrt{34}}{10}+\frac{1}{5}
Divide 4+2\sqrt{34}\approx 15.66190379 by 20.
w=\frac{4-2\sqrt{34}}{20}
Now solve the equation w=\frac{4±2\sqrt{34}}{20} when ± is minus. Subtract 2\sqrt{34}\approx 11.66190379 from 4.
w=-\frac{\sqrt{34}}{10}+\frac{1}{5}
Divide 4-2\sqrt{34}\approx -7.66190379 by 20.
10w^{2}-4w-3=10\left(w-\left(\frac{\sqrt{34}}{10}+\frac{1}{5}\right)\right)\left(w-\left(-\frac{\sqrt{34}}{10}+\frac{1}{5}\right)\right)
Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{1}{5}+\frac{\sqrt{34}}{10}\approx 0.783095189 for x_{1} and \frac{1}{5}-\frac{\sqrt{34}}{10}\approx -0.383095189 for x_{2}.