WITHOUT USING QUADRATIC FORMULA please solve x^2-7x+5 = 0?

x^2-7x=-5

Add (-7/2)^2 to both sides.

x^2-7x+49/4=-5+49/4

(x-7/2)^2=-20/4+49/4

(x-7/2)^2=29/4

x-7/2=+radical29/2 or x-7/2=-radical29/2

x=7/2=+-radical29/2

x=(7 plus minus square root of 29)/2

ax^2+bx+c=0

in this case a=1 b=-7 c=5

(x-A)(x-B)=x^2-Bx-Ax+AB=x^2-x(A+B)+AB

so you are looking for two numbers such that A+B=7 and A*B=5

but by the rational root theorem, the candidate roots are 5,1,-5,-1

try some combos:

5+1=6 and 5*1=5

5-1=4 and 5(-1)=-5

-5+1=-4 and -5(1)=-5

-5-1=-6 and (-5)(-1)=5

so none of the rational root possibilities work. The solution is irrational and needs to be solved by the quadratic equation which is simlply completing the square with variables.

To complete the square:

(x-w)^2=x^2+-2xw+w^2

add and subtract w^2

by looking at like terms, -2w=-7 so w=7/2

and w^2=49/4 so the equtoin becomes:

x^2-7x+49/4-49/4+5=0

(x-7/2)^2-49/4+20/4=0

(x-7/2)^2=29/4

x-7/2=+/-sqrt(29)/2

x=(7 +/- sqrt(29))/2

Well, like someone else has said, you have to complete the square:

x^2-7x+___=-5+___

The theory is to make the left side a perfect square. Now, when you have (x+a)^2, you know that the solution will always be x^2+2a+a^2. So, in this instance, 2a=-7, meaning a=-7/2 and a^2=49/4. Therefore, you add 49/4 to both sides

x^2-7x+49/4=-5+49/4

Now you can factor the left side and simplify the right.

(x-7/2)^2=29/4

x-7/2=±sqrt(29/4)

x=7/2±sqrt(29)/2

x=[7±sqrt(29)]/2

x² - 7x = - 5

x² - 7x + 49/4 = - 5 + 49/4

(x - 7/2)² = - 20/4 + 49/4

(x - 7/2)² = 29/4

x - 7/2 = ± √29/2

x = 7/2 ± √29/2

x = (1/2) ( 7 ± √29 )

two solutions: 10 and -3 note: divide by 2 after doing everything else 1.)7 plus minus radical 7^2-4(1)(-30) divided by 2 2.)7 plus minus radical 49+120 divided by 2 3.)7 plus minus radical 169 divided by 2 4.)7 plus minus 13 divided by 2 5.) first solution: 20 divided by 2=10 6.) second solution: -6 divided by 2=6

First, identify a, b & c.

ax^2+bx+c=0

a=1

b=-7

c=5

then, solve by using quadratic formula

x=[-b ±√(-b²-4(a)(c))]÷2(a)

x=[-(-7) ±√(-7²-4(1)(5))]÷2(1)

=[7±√(49-20)]÷2

=[7±√29]÷2

=(7±5.385)÷2

x=(7-5.385)÷2

=1.615÷2

=0.8075

x=(7+5.385)÷2

=12.385÷2

=6.1925

hence, x = 0.8075, 6.1925

Try Purple Math.com!!

complete the square.

complete the square:

http://www.purplemath.com/modules/sqrquad.htm

x(x-7) = -5

x = -5

x-7 = -5

x = 2

answer: x = 5, x = 2