X 2 6x 16 0
$\exponential{(x)}{2} + 6 ten = xvi $
x=-8
x=2
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ten^{2}+6x-16=0
Subtract sixteen from both sides.
a+b=half dozen ab=-sixteen
To solve the equation, cistron 10^{2}+6x-16 using formula x^{2}+\left(a+b\right)x+ab=\left(x+a\right)\left(x+b\right). To find a and b, fix a system to be solved.
-1,sixteen -2,8 -4,4
Since ab is negative, a and b accept the opposite signs. Since a+b is positive, the positive number has greater absolute value than the negative. List all such integer pairs that requite product -xvi.
-1+xvi=15 -two+8=6 -4+four=0
Calculate the sum for each pair.
a=-2 b=eight
The solution is the pair that gives sum half-dozen.
\left(x-2\right)\left(x+8\right)
Rewrite factored expression \left(ten+a\correct)\left(x+b\right) using the obtained values.
x=ii x=-8
To observe equation solutions, solve x-ii=0 and x+8=0.
x^{2}+6x-16=0
Subtract 16 from both sides.
a+b=6 ab=i\left(-sixteen\correct)=-xvi
To solve the equation, factor the left hand side by grouping. First, left hand side needs to be rewritten as x^{2}+ax+bx-xvi. To detect a and b, set a system to exist solved.
-1,16 -ii,8 -iv,four
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 -sixteen.
-1+16=xv -2+eight=6 -iv+4=0
Calculate the sum for each pair.
a=-ii b=8
The solution is the pair that gives sum 6.
\left(x^{2}-2x\correct)+\left(8x-16\right)
Rewrite 10^{2}+6x-16 as \left(ten^{2}-2x\right)+\left(8x-xvi\right).
x\left(ten-2\right)+eight\left(x-ii\correct)
Factor out x in the first and eight in the second grouping.
\left(x-2\right)\left(x+8\right)
Gene out mutual term x-2 by using distributive property.
x=2 x=-eight
To observe equation solutions, solve 10-2=0 and x+eight=0.
10^{2}+6x=16
All equations of the form ax^{2}+bx+c=0 tin be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives 2 solutions, 1 when ± is improver and i when it is subtraction.
x^{2}+6x-xvi=16-16
Decrease sixteen from both sides of the equation.
x^{2}+6x-16=0
Subtracting sixteen from itself leaves 0.
x=\frac{-6±\sqrt{6^{2}-four\left(-xvi\right)}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute one for a, six for b, and -xvi for c in the quadratic formula, \frac{-b±\sqrt{b^{ii}-4ac}}{2a}.
x=\frac{-6±\sqrt{36-four\left(-16\right)}}{ii}
Square six.
x=\frac{-6±\sqrt{36+64}}{2}
Multiply -iv times -sixteen.
x=\frac{-6±\sqrt{100}}{two}
Add 36 to 64.
x=\frac{-6±x}{two}
Take the square root of 100.
x=\frac{iv}{2}
Now solve the equation 10=\frac{-6±10}{2} when ± is plus. Add together -6 to 10.
x=\frac{-16}{ii}
At present solve the equation x=\frac{-half-dozen±10}{2} when ± is minus. Decrease 10 from -6.
x=2 x=-viii
The equation is now solved.
x^{2}+6x=sixteen
Quadratic equations such as this one can be solved by completing the square. In club to consummate the square, the equation must first be in the form x^{2}+bx=c.
x^{2}+6x+three^{2}=xvi+iii^{two}
Dissever 6, the coefficient of the x term, past 2 to get 3. Then add the foursquare of three to both sides of the equation. This step makes the left mitt side of the equation a perfect square.
x^{2}+6x+9=16+nine
Square 3.
x^{2}+6x+9=25
Add together 16 to 9.
\left(x+3\correct)^{ii}=25
Factor x^{2}+6x+9. In full general, when x^{ii}+bx+c is a perfect foursquare, it can always be factored as \left(x+\frac{b}{two}\right)^{2}.
\sqrt{\left(x+3\correct)^{two}}=\sqrt{25}
Have the foursquare root of both sides of the equation.
x=two 10=-8
Subtract 3 from both sides of the equation.
X 2 6x 16 0,
Source: https://mathsolver.microsoft.com/en/solve-problem/%7B%20x%20%20%7D%5E%7B%202%20%20%7D%20%20%2B6x%20%3D%20%2016
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