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w^{2}+8w-10-10=0
Subtract 10 from both sides.
w^{2}+8w-20=0
Subtract 10 from -10 to get -20.
a+b=8 ab=-20
To solve the equation, factor w^{2}+8w-20 using formula w^{2}+\left(a+b\right)w+ab=\left(w+a\right)\left(w+b\right). To find a and b, set up a system to be solved.
-1,20 -2,10 -4,5
Since ab is negative, a and b have the opposite signs. Since a+b is positive, the positive number has greater absolute value than the negative. List all such integer pairs that give product -20.
-1+20=19 -2+10=8 -4+5=1
Calculate the sum for each pair.
a=-2 b=10
The solution is the pair that gives sum 8.
\left(w-2\right)\left(w+10\right)
Rewrite factored expression \left(w+a\right)\left(w+b\right) using the obtained values.
w=2 w=-10
To find equation solutions, solve w-2=0 and w+10=0.
w^{2}+8w-10-10=0
Subtract 10 from both sides.
w^{2}+8w-20=0
Subtract 10 from -10 to get -20.
a+b=8 ab=1\left(-20\right)=-20
To solve the equation, factor the left hand side by grouping. First, left hand side needs to be rewritten as w^{2}+aw+bw-20. To find a and b, set up a system to be solved.
-1,20 -2,10 -4,5
Since ab is negative, a and b have the opposite signs. Since a+b is positive, the positive number has greater absolute value than the negative. List all such integer pairs that give product -20.
-1+20=19 -2+10=8 -4+5=1
Calculate the sum for each pair.
a=-2 b=10
The solution is the pair that gives sum 8.
\left(w^{2}-2w\right)+\left(10w-20\right)
Rewrite w^{2}+8w-20 as \left(w^{2}-2w\right)+\left(10w-20\right).
w\left(w-2\right)+10\left(w-2\right)
Factor out w in the first and 10 in the second group.
\left(w-2\right)\left(w+10\right)
Factor out common term w-2 by using distributive property.
w=2 w=-10
To find equation solutions, solve w-2=0 and w+10=0.
w^{2}+8w-10=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^{2}+8w-10-10=10-10
Subtract 10 from both sides of the equation.
w^{2}+8w-10-10=0
Subtracting 10 from itself leaves 0.
w^{2}+8w-20=0
Subtract 10 from -10.
w=\frac{-8±\sqrt{8^{2}-4\left(-20\right)}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 8 for b, and -20 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
w=\frac{-8±\sqrt{64-4\left(-20\right)}}{2}
Square 8.
w=\frac{-8±\sqrt{64+80}}{2}
Multiply -4 times -20.
w=\frac{-8±\sqrt{144}}{2}
Add 64 to 80.
w=\frac{-8±12}{2}
Take the square root of 144.
w=\frac{4}{2}
Now solve the equation w=\frac{-8±12}{2} when ± is plus. Add -8 to 12.
w=2
Divide 4 by 2.
w=-\frac{20}{2}
Now solve the equation w=\frac{-8±12}{2} when ± is minus. Subtract 12 from -8.
w=-10
Divide -20 by 2.
w=2 w=-10
The equation is now solved.
w^{2}+8w-10=10
Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.
w^{2}+8w-10-\left(-10\right)=10-\left(-10\right)
Add 10 to both sides of the equation.
w^{2}+8w=10-\left(-10\right)
Subtracting -10 from itself leaves 0.
w^{2}+8w=20
Subtract -10 from 10.
w^{2}+8w+4^{2}=20+4^{2}
Divide 8, the coefficient of the x term, by 2 to get 4. Then add the square of 4 to both sides of the equation. This step makes the left hand side of the equation a perfect square.
w^{2}+8w+16=20+16
Square 4.
w^{2}+8w+16=36
Add 20 to 16.
\left(w+4\right)^{2}=36
Factor w^{2}+8w+16. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.
\sqrt{\left(w+4\right)^{2}}=\sqrt{36}
Take the square root of both sides of the equation.
w+4=6 w+4=-6
Simplify.
w=2 w=-10
Subtract 4 from both sides of the equation.