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Solve the quadratic equation by completing the square. -10x^2 - 2x + 3=0

User Ryan Her
by
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1 Answer

19 votes
19 votes

Answer: hope it helps

Explanation:

STEP

1

:

Equation at the end of step 1

((2•5x2) - 2x) - 3 = 0

STEP

2

:

Trying to factor by splitting the middle term

2.1 Factoring 10x2-2x-3

The first term is, 10x2 its coefficient is 10 .

The middle term is, -2x its coefficient is -2 .

The last term, "the constant", is -3

Step-1 : Multiply the coefficient of the first term by the constant 10 • -3 = -30

Step-2 : Find two factors of -30 whose sum equals the coefficient of the middle term, which is -2 .

-30 + 1 = -29

-15 + 2 = -13

-10 + 3 = -7

-6 + 5 = -1

-5 + 6 = 1

-3 + 10 = 7

-2 + 15 = 13

-1 + 30 = 29

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step

2

:

10x2 - 2x - 3 = 0

STEP

3

:

Parabola, Finding the Vertex:

3.1 Find the Vertex of y = 10x2-2x-3

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, 10 , 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, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 0.1000

Plugging into the parabola formula 0.1000 for x we can calculate the y -coordinate :

y = 10.0 * 0.10 * 0.10 - 2.0 * 0.10 - 3.0

or y = -3.100

User Markoffden
by
2.9k points
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