2×2-14x+24=0

Factor 2 out of 2×2-14x+24.

Factor 2 out of 2×2.

2(x2)-14x+24=0

Factor 2 out of -14x.

2(x2)+2(-7x)+24=0

Factor 2 out of 24.

2×2+2(-7x)+2⋅12=0

Factor 2 out of 2×2+2(-7x).

2(x2-7x)+2⋅12=0

Factor 2 out of 2(x2-7x)+2⋅12.

2(x2-7x+12)=0

2(x2-7x+12)=0

Factor.

Factor x2-7x+12 using the AC method.

Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is 12 and whose sum is -7.

-4,-3

Write the factored form using these integers.

2((x-4)(x-3))=0

2((x-4)(x-3))=0

Remove unnecessary parentheses.

2(x-4)(x-3)=0

2(x-4)(x-3)=0

2(x-4)(x-3)=0

Divide each term in 2(x-4)(x-3)=0 by 2.

2(x-4)(x-3)2=02

Simplify 2(x-4)(x-3)2.

Cancel the common factor of 2.

Cancel the common factor.

2(x-4)(x-3)2=02

Divide (x-4)(x-3) by 1.

(x-4)(x-3)=02

(x-4)(x-3)=02

Expand (x-4)(x-3) using the FOIL Method.

Apply the distributive property.

x(x-3)-4(x-3)=02

Apply the distributive property.

x⋅x+x⋅-3-4(x-3)=02

Apply the distributive property.

x⋅x+x⋅-3-4x-4⋅-3=02

x⋅x+x⋅-3-4x-4⋅-3=02

Simplify and combine like terms.

Simplify each term.

Multiply x by x.

x2+x⋅-3-4x-4⋅-3=02

Move -3 to the left of x.

x2-3⋅x-4x-4⋅-3=02

Multiply -4 by -3.

x2-3x-4x+12=02

x2-3x-4x+12=02

Subtract 4x from -3x.

x2-7x+12=02

x2-7x+12=02

x2-7x+12=02

Divide 0 by 2.

x2-7x+12=0

x2-7x+12=0

Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is 12 and whose sum is -7.

-4,-3

Write the factored form using these integers.

(x-4)(x-3)=0

(x-4)(x-3)=0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

x-4=0

x-3=0

Set the first factor equal to 0.

x-4=0

Add 4 to both sides of the equation.

x=4

x=4

Set the next factor equal to 0.

x-3=0

Add 3 to both sides of the equation.

x=3

x=3

The final solution is all the values that make (x-4)(x-3)=0 true.

x=4,3

Solve using the Square Root Property 2x^2-14x+24=0