Question

X√2+32x-219 solve it by spliting the middle term

Answer 1

Step-by-step explanation:

Factoring x2+32x-219

The first term is, x2 its coefficient is 1 .

The middle term is, +32x its coefficient is 32 .

The last term, "the constant", is -219

Step-1 : Multiply the coefficient of the first term by the constant 1 • -219 = -219

Step-2 : Find two factors of -219 whose sum equals the coefficient of the middle term, which is 32 .

-219 + 1 = -218

-73 + 3 = -70

-3 + 73 = 70

-1 + 219 = 218

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step

1

:

x2 + 32x - 219 = 0

STEP

2

:

Parabola, Finding the Vertex:

2.1 Find the Vertex of y = x2+32x-219

Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 1 , is positive (greater than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such1900 = √ 2•2•5•5•19 =2•5•√ 19 =

± 10 • √ 19

√ 19 , rounded to 4 decimal digits, is 4.3589

So now we are looking at:

x = ( -32 ± 10 • 4.359 ) / 2

Two real solutions:

x =(-32+√1900)/2=-16+5√ 19 = 5.794

or:

x =(-32-√1900)/2=-16-5√ 19 = -37.794