Factor x^2+ x

     
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.

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This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, -1 for b, and -1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
How do you find the value of the discriminant and determine the nature of the roots \displaystyle-{2}{x}^{{2}}-{x}-{1}={0} ?
https://socratic.org/questions/how-do-you-find-the-value-of-the-discriminant-and-determine-the-nature-of-the-ro-1
-7, no real rootsExplanation:The discriminant is found using the equation\displaystyle{b}^{{2}}-{4}{a}{c} . Substitute the values from your equation into this one so:a = -2 b = -1 c = -1the ...
-x2-4x-1=0 Two solutions were found : x =(4-√12)/-2=2+√ 3 = -0.268 x =(4+√12)/-2=2-√ 3 = -3.732 Step by step solution : Step 1 : Step 2 :Pulling out like terms : 2.1 Pull out like ...
-x2-9x-1=0 Two solutions were found : x =(9-√77)/-2=-0.113 x =(9+√77)/-2=-8.887 Step by step solution : Step 1 : Step 2 :Pulling out like terms : 2.1 Pull out like factors : -x2 ...
-x2-x-10=0 Two solutions were found : x =(1-√-39)/-2=1/-2+i/2√ 39 = -0.5000-3.1225i x =(1+√-39)/-2=1/-2-i/2√ 39 = -0.5000+3.1225i Step by step solution : Step 1 : Step 2 :Pulling out like ...
-x2-x-13=0 Two solutions were found : x =(1-√-51)/-2=1/-2+i/2√ 51 = -0.5000-3.5707i x =(1+√-51)/-2=1/-2-i/2√ 51 = -0.5000+3.5707i Step by step solution : Step 1 : Step 2 :Pulling out like ...

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-x2-x-14=0 Two solutions were found : x =(1-√-55)/-2=1/-2+i/2√ 55 = -0.5000-3.7081i x =(1+√-55)/-2=1/-2-i/2√ 55 = -0.5000+3.7081i Step by step solution : Step 1 : Step 2 :Pulling out like ...
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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.
This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, -1 for b, and -1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
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.
Divide 1, the coefficient of the x term, by 2 to get \frac{1}{2}. Then add the square of \frac{1}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.
Factor x^{2}+x+\frac{1}{4}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

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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.
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
Two numbers r and s sum up to -1 exactly when the average of the two numbers is \frac{1}{2}*-1 = -\frac{1}{2}. 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.
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