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0+10x+16=0
Anything times zero gives zero.
16+10x=0
Add 0 and 16 to get 16.
10x=-16
Subtract 16 from both sides. Anything subtracted from zero gives its negation.
x=\frac{-16}{10}
Divide both sides by 10.
x=-\frac{8}{5}
Reduce the fraction \frac{-16}{10} to lowest terms by extracting and canceling out 2.
x ^ 2 +10x +16 = 0
Quadratic equations such as this one can be solved by a new direct factoring method that does not require guess work. To use the direct factoring method, the equation must be in the form x^2+Bx+C=0.
r + s = -10 rs = 16
Let r and s be the factors for the quadratic equation such that x^2+Bx+C=(x−r)(x−s) where sum of factors (r+s)=−B and the product of factors rs = C
r = -5 - u s = -5 + u
Two numbers r and s sum up to -10 exactly when the average of the two numbers is \frac{1}{2}*-10 = -5. You can also see that the midpoint of r and s corresponds to the axis of symmetry of the parabola represented by the quadratic equation y=x^2+Bx+C. The values of r and s are equidistant from the center by an unknown quantity u. Express r and s with respect to variable u. <div style='padding: 8px'><img src='https://opalmath.azureedge.net/customsolver/quadraticgraph.png' style='width: 100%;max-width: 700px' /></div>
(-5 - u) (-5 + u) = 16
To solve for unknown quantity u, substitute these in the product equation rs = 16
25 - u^2 = 16
Simplify by expanding (a -b) (a + b) = a^2 – b^2
-u^2 = 16-25 = -9
Simplify the expression by subtracting 25 on both sides
u^2 = 9 u = \pm\sqrt{9} = \pm 3
Simplify the expression by multiplying -1 on both sides and take the square root to obtain the value of unknown variable u
r =-5 - 3 = -8 s = -5 + 3 = -2
The factors r and s are the solutions to the quadratic equation. Substitute the value of u to compute the r and s.