Explain how to solve a quadratic equation by:?

Question

a. Square root method
Use (x-2)^2-9= 0 to explain

b. Quadratic formula method
Use x^2-10+3x=0 to explain

Answer 1

a. (x - 2)^2 - 9 = 0

Add 9 to isolate the square

(x - 2)^2 = 9

Take the square root of both sides

x - 2 = +/- 3

Solve for x

x = 2 +/- 3

Simplify

x = 2 + 3 = 5
x = 2 - 3 = -1

The solutions are -1 and 5.

b. x^2 - 10 + 3x = 0

Arrange in descending order

x^2 + 3x - 10 = 0

a = 1, b = 3, c = -10

Substitute into the formula:

x = [ -b +/- SQRT (b^2 - 4ac) ] / (2a)

x = [ -3 +/- SQRT (3^2 - 4(1)(-10)) ] / (2(1))

Simplify

x = [ -3 +/- SQRT (9 + 40) ] / 2

x = [ -3 +/- SQRT (49) ] / 2

x = [ -3 +/- 7 ] / 2

x = [-3 + 7] / 2 = 2

x = [-3 - 7 ] / 2 = -5

The solutions are -5 and 2.

Answer 2

A) First, set all constants to one side of the equation, and leave all X terms on the other side of the equation.
-> (x-2)^2 - 9 = 0
-> (x-2)^2 = 9

Then, take the square root of each side:
-> sqrt[(x-2)^2] = sqrt(9)
-> x-2 = 3

Then move the rest of the constants to the other side to isolate the x term and you're done:
-> x = 5

B) We use the formula x = [-b +- sqrt[(b^2) - 4ac]] / 2a
That is, negative b, plus or minus the square root of [b squared minus 4*a*c], all divided by 2*a.

In the example given, a = 1, b = 3, c = -10

Thus, we have:
[-3 +- sqrt ((3)^2 - 4*1*(-10)] / 2*1
[-3 +- sqrt (9+40)] / 2

[-3 + 7] / 2 = 2
[-3 - 7] / 2 = -2

Now plug in both solutions to check (we always have to check our solutions obtained from the quadratic formula):
Plugging in x = 2 into the original equation works, plugging in -2 yields an inequality and hence a wrong answer (you get -6 = 6 which is false).

Thus, the answer is 2.

Answer 3

A) First u subtract 9 from both sides than when you are done with that u are practically done because the point is to have a square of a number on either right or left side. So am saying that this is a stupid example. Srry.

B) Quadratic formula is negative b +or minus square root of b square minus 4ac over 2a
when a=1
b=-10&
c=3

Answer 4

Simple.
Q1: No square root method. Just Formula method.

Here the formula used is a^2 - b^ 2 = (a + b) * ( a - b)

(x -2) ^2 - 9 = 0

= (x-2) ^2 - (3) ^2

= ( x-2 +3 ) * (x - 2 - 3)

= (x + 1) ( x - 5) = 0

Either (x + 1 ) = 0 or (x -5 ) = 0

The value of x = - 1 or + 5 Answer

Q2: Factorizing using the Quadratic Formula.

a x^2 + b x + c = 0

In the given equation,

a =1
b = +3
c = - 10

The formula is - b plus or minus root of [(b ^ 2 - 4 a*c)] divided by 2a.

Substituting the values of a, b, c in the formula, we get

-3 plus or minus [ root of (9 - 4 * 1 * (-10) ] divided by (2 * 1)

= - 3 + 0r - [(root of 9 + 40) ]divided by 2

The values of x are

( - 3 + 7) / 2 = + 2............... Answer

or ( - 3 - 7) / 2 = - 10 / 2 = - 5.... Answer

So, the value of x = +2 or - 5 ANSWER

Clear?

Answer 5

For a) put the add 9 to both side and then square rout both sides. you get x-2=3 or x= 5
For b) just plug in to the quadratic equation with a=1 b=3 and c=-10

Answer 6

Question a)
(x - 2)² = 9
(x - 2) = ± 3
x = 2 ± 3
x = - 1, x = 5
Question b)
x² + 3x - 10 = 0
x = [ -3 ± √49 ] / 2
x = [ -3 ± 7 ] / 2
x = 2, x = - 5