2×2+4=9x

Subtract 9x from both sides of the equation.

2×2+4-9x=0

Reorder terms.

2×2-9x+4=0

For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=2⋅4=8 and whose sum is b=-9.

Factor -9 out of -9x.

2×2-9x+4=0

Rewrite -9 as -1 plus -8

2×2+(-1-8)x+4=0

Apply the distributive property.

2×2-1x-8x+4=0

2×2-1x-8x+4=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(2×2-1x)-8x+4=0

Factor out the greatest common factor (GCF) from each group.

x(2x-1)-4(2x-1)=0

x(2x-1)-4(2x-1)=0

Factor the polynomial by factoring out the greatest common factor, 2x-1.

(2x-1)(x-4)=0

(2x-1)(x-4)=0

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

2x-1=0

x-4=0

Set the first factor equal to 0.

2x-1=0

Add 1 to both sides of the equation.

2x=1

Divide each term by 2 and simplify.

Divide each term in 2x=1 by 2.

2×2=12

Cancel the common factor of 2.

Cancel the common factor.

2×2=12

Divide x by 1.

x=12

x=12

x=12

x=12

Set the next factor equal to 0.

x-4=0

Add 4 to both sides of the equation.

x=4

x=4

The final solution is all the values that make (2x-1)(x-4)=0 true.

x=12,4

Solve using the Square Root Property 2x^2+4=9x