Step by action solution :

Step 1 :

Step 2 :

Pulling out like terms :2.1 pull out favor factors:-x2 - 6x - 8=-1•(x2 + 6x + 8)

Trying to variable by separating the middle term

2.2Factoring x2 + 6x + 8 The first term is, x2 its coefficient is 1.The middle term is, +6x its coefficient is 6.The last term, "the constant", is +8Step-1 : main point the coefficient the the an initial term by the constant 1•8=8Step-2 : uncover two components of 8 whose sum equates to the coefficient that the center term, which is 6.

2+4=6That"s it

Step-3 : Rewrite the polynomial splitting the center term utilizing the two components found in step2above, 2 and also 4x2 + 2x+4x + 8Step-4 : add up the very first 2 terms, pulling out favor factors:x•(x+2) add up the last 2 terms, pulling out usual factors:4•(x+2) Step-5:Add up the four terms the step4:(x+4)•(x+2)Which is the preferred factorization

Equation in ~ the end of step 2 :

(-x - 4) • (x + 2) = 0

Step 3 :

Theory - roots of a product :3.1 A product of numerous terms equals zero.When a product of 2 or much more terms amounts to zero, then at the very least one that the terms must be zero.We shall currently solve every term = 0 separatelyIn various other words, we are going to solve as plenty of equations together there space terms in the productAny equipment of hatchet = 0 solves product = 0 together well.

Solving a single Variable Equation:

3.2Solve:-x-4 = 0Add 4 to both political parties of the equation:-x = 4 main point both sides of the equation by (-1) : x = -4

Solving a solitary Variable Equation:

3.3Solve:x+2 = 0Subtract 2 from both sides of the equation:x = -2

Supplement : addressing Quadratic Equation Directly

Solving x2+6x+8 = 0 straight Earlier us factored this polynomial by separating the middle term. Permit us now solve the equation by completing The Square and also by utilizing the Quadratic Formula

Parabola, finding the Vertex:

4.1Find the crest ofy = x2+6x+8Parabolas have a greatest or a lowest allude called the Vertex.Our parabola opens up up and appropriately has a lowest point (AKA absolute minimum).We understand this even before plotting "y" due to the fact that the coefficient of the very first term,1, is hopeful (greater 보다 zero).Each parabola has actually a vertical heat of symmetry that passes with its vertex. Because of this symmetry, the line of the opposite would, for example, pass v the midpoint the the 2 x-intercepts (roots or solutions) that the parabola. That is, if the parabola has indeed two actual solutions.Parabolas deserve to model numerous real life situations, such as the height above ground, of an item thrown upward, after some duration of time. The crest of the parabola can carry out us through information, such as the maximum elevation that object, thrown upwards, have the right to reach. Therefore we desire to be able to find the works with of the vertex.For any type of parabola,Ax2+Bx+C,the x-coordinate that the vertex is provided by -B/(2A). In our case the x name: coordinates is -3.0000Plugging right into the parabola formula -3.0000 for x we have the right to calculate the y-coordinate:y = 1.0 * -3.00 * -3.00 + 6.0 * -3.00 + 8.0 or y = -1.000

Parabola, Graphing Vertex and also X-Intercepts :

Root plot because that : y = x2+6x+8 Axis of the opposite (dashed) x=-3.00 Vertex at x,y = -3.00,-1.00 x-Intercepts (Roots) : source 1 at x,y = -4.00, 0.00 source 2 at x,y = -2.00, 0.00

Solve Quadratic Equation by completing The Square

4.2Solvingx2+6x+8 = 0 by perfect The Square.Subtract 8 from both side of the equation :x2+6x = -8Now the clever bit: take it the coefficient that x, i m sorry is 6, division by two, providing 3, and finally square it providing 9Add 9 come both political parties of the equation :On the best hand side us have:-8+9or, (-8/1)+(9/1)The typical denominator the the two fractions is 1Adding (-8/1)+(9/1) offers 1/1So including to both sides we ultimately get:x2+6x+9 = 1Adding 9 has completed the left hand side right into a perfect square :x2+6x+9=(x+3)•(x+3)=(x+3)2 points which are equal to the exact same thing are likewise equal to one another. Sincex2+6x+9 = 1 andx2+6x+9 = (x+3)2 then, according to the regulation of transitivity,(x+3)2 = 1We"ll refer to this Equation as Eq.

You are watching: If x2 - 6x + 8 = 0, then x - 4 = 0 or x - 2 = 0.

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#4.2.1 The Square source Principle says that when two things space equal, your square roots space equal.Note the the square source of(x+3)2 is(x+3)2/2=(x+3)1=x+3Now, using the Square source Principle to Eq.#4.2.1 we get:x+3= √ 1 Subtract 3 native both political parties to obtain:x = -3 + √ 1 due to the fact that a square root has two values, one positive and also the other negativex2 + 6x + 8 = 0has 2 solutions:x = -3 + √ 1 orx = -3 - √ 1

Solve Quadratic Equation making use of the Quadratic Formula

4.3Solvingx2+6x+8 = 0 by the Quadratic Formula.According to the Quadratic Formula,x, the systems forAx2+Bx+C= 0 , whereby A, B and C are numbers, often referred to as coefficients, is provided by :-B± √B2-4ACx = ————————2A In our case,A= 1B= 6C= 8 Accordingly,B2-4AC=36 - 32 =4Applying the quadratic formula : -6 ± √ 4 x=—————2Can √ 4 be streamlined ?Yes!The prime factorization the 4is2•2 To be able to remove something indigenous under the radical, there need to be 2 instances of it (because we room taking a square i.e. Second root).√ 4 =√2•2 =±2 •√ 1 =±2 So now we room looking at:x=(-6±2)/2Two real solutions:x =(-6+√4)/2=-3+= -2.000 or:x =(-6-√4)/2=-3-= -4.000