please can someone solve these by using completing the square?

Question

x (squared) + 10x +21 = 0

x (squared) + 4x -3 = 0

Answer 1

1. Complete the square... x^2 + 10x +21 = 0

First: subtract the whole number from both sides (when you move a term to the opposite side, always use the opposite sign).

x^2+10x+21 - 21 = 0 - 21
x^2 + 10x___ = -21

Sec: take the 2nd term & divide it by 2 or, multiply it by (1/2) & square the result. Add the final result with both sides of the equation.

10/2 = 5 > 5^2 = 25

x^2 + 10x + 25 = -21 + 25
x^2 + 10x + 25 = 4

Third: factor the expression & you should get...

(x+5)(x+5) = 4
(x+5)^2 = 4

Fourth: eliminate the exponent - find the square root of both sides.

V`(x+5)^2 = +/- V`(4)
x+5 = +/- 2

*Subtract 5 from both sides - there are 2 solutions.

a. 2 - 5 = -3

b. - 2 - 5 = -7

Solutions: -3, -7

Answer 2

x^2 + 10x +21 = 0
x^2 + 10x = -21
x^2 + 10x + 25 = -21 +25
x^2 + 10x + 25 = 4 Next, factor the left side.
(x + 5)^2 = 4
x +5 = +-sqrt (4)
x + 5 = +-2
x = +-2 -5
x = -3 or -7

You can also check your answers for this first quadratic by factoring. x^2 + 10x +21 = 0 is the same as (x+7)(x+3)=0 so -7 and -3 are the solutions.


x^2 + 4x -3 = 0
x^2 +4x +4 = 3 + 4 = 7
(x+2)^2 = 7
x = +-sqrt(7) -2

Answer 3

(x² + 10x + 25) + 21 - 25 = 0
(x + 5)² = 4
x + 5 = ±√4
x = - 5 ± 2
x = - 3 , - 7

x² + 4x + 4 = 3 + 4
(x + 2)² = 7
x + 2 = ± √7
x = - 2 ± √7

Answer 4

x^2 +10x +21=0 add 4 to both sides
x^2 +10x +25 = 4 take square root of both sides
(x +5)^2 = 4
(x +5 ) =2 or (x +5 ) = -2
x= 2 -5 or x = -2 -5
x = -3 or x = -7


x^2 +4x-3 = 0 add 7 to both sides
x^2 +4x +4 =7
(x +2)^2 =7 take square root of both sides
x+2 =square root+7 or x+2=square root -7
x = -2 square root7 orx = -2 square root +7

Answer 5

okay so the first step of completing the square is to put all the x values on one side

x^2 + 10x = -21

then you can complete the square

(x + 5)^2 -25 = -21

this is done by halving the co efficient of x, ie. 10/2 = 5 then placing them in brackets with x, however you have an extra value of 5*5 if you expand the brackets therefore you need to minus this, hence -25. then you can collect the terms

(x+5)^2= -21 + 25
(x+5)^2= 4

then to get rid of the squared sign you square root each side

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

apply these rules to the second question:

(x+2)^2 - 4 = 3
(x+2)^2 = 7
x+2 = (+ or - root)7
x=-2 ( +or - root) 7

Answer 6

x^2+10x+21=0
=> x^2+10x= -21
=> (x)^2+2*x*5+(5)^2=-21+25[adding (5)^2 or 25 to both sides]
=>(x+5)^2=4
=>x+5=+-2(square-rooting both sides]
=>x=-5+-2
x= -3 or -7 ans
2)x^2+4x= -3
=>x^2+4x+4= -3+4[adding 4 to both sides]
=>(x+2)^2=1
=>x+2=+-1[square-rooting both sides]
=>x= -2+-1
x= -1 or -3 ans

Answer 7

x^2 + 10x + 21 = 0
(x + 5)^2 - 4 = 0
(x + 5)^2 = 4
x + 5 = 2 or -2
x = -3 or -7

x^2 + 4x - 3 = 0
(x + 2)^2 - 7 = 0
(x + 2)^2 = 7
x + 2 = SQRT 7
x = SQRT 7 - 2
x = 0.646 or -4.646

Answer 8

X squared + 10 X + 21

(x)the whole squared + 2(5)x + (5)square-(5)square+21

(x+5)whole squared =4

therefore taking square root

x+5= + or – 2
x= -7 or -3

Answer 9

This would be doing your homework for you, but...

(x+5)^2 -4 = 0
(x+5)^2 = 4
x+5 = +/-2
x= -3 or -7

(x+2)^2 - 7 = 0
(x+2)^2 = 7
x + 2 = sq. root 7
x = (+/- sq. root 7) - 2
x = 0.65 or -4.65 (2 d.p.)

Answer 10

x^2+10= -21
(x+5)^2=-21+25
(x+5)^2=4
x+5=+-2
x=+-2-5
x=-3,x=-7