Solve using quadratic equation(equation inside)?

(2p - 3)(p - 2) = (p - 5)(p - 4)
(2p - 3)(p - 2) - (p - 5)(p - 4) = 0
2p² - 7p + 6 - p² + 9p - 20 = 0
p² + 2p = 14
(p + 1)² = 15
p = -1 ± √15

Answer: p = -1 ± √15

query variety a million : For this equation x^2 - 7*x - a million = - 7 , answer here questions : A. discover the roots employing Quadratic formulation ! B. Use factorization to discover the basis of the equation ! C. Use ending up the sq. to discover the basis of the equation ! answer variety a million : First, we ought to teach equation : x^2 - 7*x - a million = - 7 , right into a*x^2+b*x+c=0 type. x^2 - 7*x - a million = - 7 , pass each little thing interior the excellent hand section, to the left hand portion of the equation <=> x^2 - 7*x - a million - ( - 7 ) = 0 , that's an identical with <=> x^2 - 7*x - a million + ( 7 ) =0 , now open the bracket and we get <=> x^2 - 7*x + 6 = 0 The equation x^2 - 7*x + 6 = 0 is already in a*x^2+b*x+c=0 type. In that type, we are able to surely derive that the value of a = a million, b = -7, c = 6. 1A. discover the roots employing Quadratic formulation ! Use the formulation, x1 = (-b+sqrt(b^2-4*a*c))/(2*a) and x2 = (-b-sqrt(b^2-4*a*c))/(2*a) We had understand that a = a million, b = -7 and c = 6, we ought to subtitute a,b,c interior the abc formulation, with thos values. Which produce x1 = (-(-7) + sqrt( (-7)^2 - 4 * (a million)*(6)))/(2*a million) and x2 = (-(-7) - sqrt( (-7)^2 - 4 * (a million)*(6)))/(2*a million) that's an identical with x1 = ( 7 + sqrt( 40 9-24))/(2) and x2 = ( 7 - sqrt( 40 9-24))/(2) Which make x1 = ( 7 + sqrt( 25))/(2) and x2 = ( 7 - sqrt( 25))/(2) So we get x1 = ( 7 + 5 )/(2) and x2 = ( 7 - 5 )/(2) So we've the solutions x1 = 6 and x2 = a million 1B. Use factorization to discover the basis of the equation ! x^2 - 7*x + 6 = 0 ( x - 6 ) * ( x - a million ) = 0 The solutions are x1 = 6 and x2 = a million 1C. Use ending up the sq. to discover the basis of the equation ! x^2 - 7*x + 6 = 0 ,divide the two section with a million Then we get x^2 - 7*x + 6 = 0 , all of us understand that the coefficient of x is -7 we ought to apply the actuality that ( x + q )^2 = x^2 + 2*q*x + q^2 , and assume that q = -7/2 = -3.5 So we've make the equation into x^2 - 7*x + 12.25 - 6.25 = 0 which could be grew to become into ( x - 3.5 )^2 - 6.25 = 0 So we are able to get (( x - 3.5 ) - 2.5 ) * (( x - 3.5 ) + 2.5 ) = 0 by using employing the associative regulation we get ( x - 3.5 - 2.5 ) * ( x - 3.5 + 2.5 ) = 0 And this is an identical with ( x - 6 ) * ( x - a million ) = 0 So we've been given the solutions as x1 = 6 and x2 = a million

(2p - 3)(p - 2) = (p - 5)(p - 4)
2p(p) - 2p(2) - 3(p) + 3(2) = p(p) - p(4) - 5(p) + 5(4)
2p^2 - 4p - 3p + 6 = p^2 - 4p - 5p + 20
2p^2 - p^2 - 7p + 4p + 5p + 6 - 20 = 0
p^2 + 2p - 14 = 0
p^2 + 2p = 14
p^2 + p + p = 14
p^2 + p + p + 1 = 14 + 1
(p^2 + p) + (p + 1) = 15
p(p + 1) + 1(p + 1) = 15
(p + 1)(p + 1) = 15
(p + 1)^2 = 15
p + 1 = ±√15
p = -1 ±√15

(2p - 3) (p - 2) = (p - 5) (p - 4)
2p^2 - 7p + 6 = p^2 - 9p + 20
p^2 + 2p - 14 = 0

p = (-2 +/- (2^2 - 4*1*-14)^1/2) / 2*1
= (-2 +/- (4 + 56)^1/2) / 2
= (-2 +/- 7.75) / 2

p1 = 5.75 / 2
= 2.875

p2 = -9.75 / 2
= -4.875

(2p-3)(p-2) = (p-5)(p-4)
2p"2-7p+6 = p"2-9p+20
2p"2-7p+6-p"2+9p-20=0
p"2+2p-14=0

D = 4 - 4x1x(-14)
D = 60
VD = V60 = 2V15
so
p = (-2 + 2V15) / 2 or p = (-2 - 2V15)/2

=====>
2p^2-8p-3p+12=p^2-7p+10
p^2-4p+2=0
p=[2+&-(4-2)^1/2]
p=2+\/''2'''
&
p=2-\/'''2''''

(2p-3)(p-2)=(p-5)(p-4)
2p^2- 7p +6 = p^2- 9p +20
p^2 +2p -14 = 0
p = (-2 +/- sqrt(60))/2
= -1 +/- sqrt(15)

(2p-3)(p-2)=(p-5)(p-4)

p (p+2) = 14
p^2+2p-14=0
p = -1-sqrt(15)
p = sqrt(15)-1