### Reformatting the entry :

Changes make to her input have to not influence the solution: (1): "x2" was replaced by "x^2".## Step by action solution :

## Step 1 :

Trying to variable by splitting the center term1.1Factoring x2-2x-2 The an initial term is, x2 that coefficient is 1.The center term is, -2x the coefficient is -2.The critical term, "the constant", is -2Step-1 : main point the coefficient the the first term by the continuous 1•-2=-2Step-2 : uncover two determinants of -2 who sum equals the coefficient of the middle term, which is -2.

-2 | + | 1 | = | -1 | ||

-1 | + | 2 | = | 1 |

Observation : No 2 such components can be found !! Conclusion : Trinomial have the right to not be factored

Equation at the end of step 1 :x2 - 2x - 2 = 0

## Step 2 :

Parabola, finding the Vertex:2.1Find the peak ofy = x2-2x-2Parabolas have actually a greatest or a lowest point called the Vertex.Our parabola opens up and accordingly has a lowest suggest (AKA pure minimum).We know this even prior to plotting "y" due to the fact that the coefficient the the very first term,1, is optimistic (greater than zero).Each parabola has a vertical heat of symmetry that passes v its vertex. Thus symmetry, the line of the opposite would, because that example, pass with the midpoint of the two x-intercepts (roots or solutions) that the parabola. The is, if the parabola has indeed two genuine solutions.Parabolas can model countless real life situations, such as the height above ground, of an item thrown upward, ~ some period of time. The vertex of the parabola can provide us v information, such together the maximum elevation that object, thrown upwards, have the right to reach. Hence we desire to have the ability to find the coordinates of the vertex.For any parabola,Ax2+Bx+C,the x-coordinate the the peak is provided by -B/(2A). In our instance the x name: coordinates is 1.0000Plugging right into the parabola formula 1.0000 for x we deserve to calculate the y-coordinate:y = 1.0 * 1.00 * 1.00 - 2.0 * 1.00 - 2.0 or y = -3.000Parabola, Graphing Vertex and also X-Intercepts :Root plot because that : y = x2-2x-2 Axis of symmetry (dashed) x= 1.00 Vertex in ~ x,y = 1.00,-3.00 x-Intercepts (Roots) : source 1 at x,y = -0.73, 0.00 root 2 at x,y = 2.73, 0.00

Solve Quadratic Equation by completing The Square2.2Solvingx2-2x-2 = 0 by perfect The Square.Add 2 come both next of the equation : x2-2x = 2Now the clever bit: take the coefficient of x, which is 2, division by two, giving 1, and finally square it providing 1Add 1 to both political parties of the equation :On the right hand side us have:2+1or, (2/1)+(1/1)The typical denominator that the 2 fractions is 1Adding (2/1)+(1/1) offers 3/1So adding to both sides we ultimately get:x2-2x+1 = 3Adding 1 has actually completed the left hand side into a perfect square :x2-2x+1=(x-1)•(x-1)=(x-1)2 points which are equal to the exact same thing are also equal come one another. Sincex2-2x+1 = 3 andx2-2x+1 = (x-1)2 then, according to the law of transitivity,(x-1)2 = 3We"ll refer to this Equation as Eq.

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#2.2.1 The Square root Principle claims that when two things are equal, their square roots are equal.Note the the square source of(x-1)2 is(x-1)2/2=(x-1)1=x-1Now, applying the Square source Principle come Eq.#2.2.1 we get:x-1= √ 3 include 1 to both sides to obtain:x = 1 + √ 3 since a square root has two values, one positive and the various other negativex2 - 2x - 2 = 0has 2 solutions:x = 1 + √ 3 orx = 1 - √ 3

### Solve Quadratic Equation using the Quadratic Formula

2.3Solvingx2-2x-2 = 0 by the Quadratic Formula.According come the Quadratic Formula,x, the equipment forAx2+Bx+C= 0 , where A, B and also C space numbers, often dubbed coefficients, is given by :-B± √B2-4ACx = ————————2A In our case,A= 1B= -2C= -2 Accordingly,B2-4AC=4 - (-8) = 12Applying the quadratic formula : 2 ± √ 12 x=—————2Can √ 12 be simplified ?Yes!The prime factorization that 12is2•2•3 To have the ability to remove something indigenous under the radical, there need to be 2 instances of it (because we space taking a square i.e. Second root).√ 12 =√2•2•3 =±2 •√ 3 √ 3 , rounded to 4 decimal digits, is 1.7321So currently we space looking at:x=(2±2• 1.732 )/2Two genuine solutions:x =(2+√12)/2=1+√ 3 = 2.732 or:x =(2-√12)/2=1-√ 3 = -0.732