# Solve using the Square Root Property 3x=x^2-4

3x=x2-4
Subtract x2 from both sides of the equation.
3x-x2=-4
Move 4 to the left side of the equation by adding it to both sides.
3x-x2+4=0
Factor the left side of the equation.
Let u=x. Substitute u for all occurrences of x.
3u-u2+4
Factor by grouping.
Reorder terms.
-u2+3u+4
For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=-1⋅4=-4 and whose sum is b=3.
Factor 3 out of 3u.
-u2+3(u)+4
Rewrite 3 as -1 plus 4
-u2+(-1+4)u+4
Apply the distributive property.
-u2-1u+4u+4
-u2-1u+4u+4
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
(-u2-1u)+4u+4
Factor out the greatest common factor (GCF) from each group.
u(-u-1)-4(-u-1)
u(-u-1)-4(-u-1)
Factor the polynomial by factoring out the greatest common factor, -u-1.
(-u-1)(u-4)
(-u-1)(u-4)
Replace all occurrences of u with x.
(-x-1)(x-4)
Replace the left side with the factored expression.
(-x-1)(x-4)=0
(-x-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.
-x-1=0
x-4=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
-x-1=0
Add 1 to both sides of the equation.
-x=1
Multiply each term in -x=1 by -1
Multiply each term in -x=1 by -1.
(-x)⋅-1=1⋅-1
Multiply (-x)⋅-1.
Multiply -1 by -1.
1x=1⋅-1
Multiply x by 1.
x=1⋅-1
x=1⋅-1
Multiply -1 by 1.
x=-1
x=-1
x=-1
Set the next factor equal to 0 and solve.
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 (-x-1)(x-4)=0 true.
x=-1,4
Solve using the Square Root Property 3x=x^2-4