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The equation has two roots. With this information, we can factor the expression by substituting a= sqrt(10) and b= - sqrt(10) in the expression (x- a)(x- b). (x- sqrt(10))(x-( - sqrt(10))) ⇓ (x-sqrt(10))(x+sqrt(10))
x^2-3x-7=0
Use the Quadratic Formula: a = 1, b= - 3, c= -7
- (- a)=a
Calculate power and product
Add terms
State solutions
The equation has two roots. With this information, we can factor the expression by substituting a= 3+sqrt(37)2 and b= 3-sqrt(37)2 into the form (x- a)(x- b). (x- 3+sqrt(37)2)(x- 3-sqrt(37)2)
LHS-4=RHS-4
sqrt(LHS)=sqrt(RHS)
sqrt(- a)= isqrt(a)
Calculate root
Commutative Property of Multiplication
The equation has two roots. With this information, we can factor the expression by substituting a= 2i and b= - 2i in the form (x- a)(x- b). (x- 2i)(x-( - 2i)) ⇓ (x-2i)(x+2i)
x^2-2x+2=0
Use the Quadratic Formula: a = 1, b= -2, c= 2
- (- a)=a
Calculate power and product
Subtract term
sqrt(- a)= isqrt(a)
Calculate root
Commutative Property of Multiplication
State solutions
(I), (II): Calculate quotient
The equation has two roots. With this information, we can factor the expression by substituting a= 1+i and b= 1-i in the form (x- a)(x- b). (x-( 1+i))(x-( 1-i))