# Solve using the Square Root Property 3x^2+7x-24=13x

3×2+7x-24=13x
Move all terms containing x to the left side of the equation.
Subtract 13x from both sides of the equation.
3×2+7x-24-13x=0
Subtract 13x from 7x.
3×2-6x-24=0
3×2-6x-24=0
Factor the left side of the equation.
Factor 3 out of 3×2-6x-24.
Factor 3 out of 3×2.
3(x2)-6x-24=0
Factor 3 out of -6x.
3(x2)+3(-2x)-24=0
Factor 3 out of -24.
3×2+3(-2x)+3⋅-8=0
Factor 3 out of 3×2+3(-2x).
3(x2-2x)+3⋅-8=0
Factor 3 out of 3(x2-2x)+3⋅-8.
3(x2-2x-8)=0
3(x2-2x-8)=0
Factor.
Factor x2-2x-8 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 -8 and whose sum is -2.
-4,2
Write the factored form using these integers.
3((x-4)(x+2))=0
3((x-4)(x+2))=0
Remove unnecessary parentheses.
3(x-4)(x+2)=0
3(x-4)(x+2)=0
3(x-4)(x+2)=0
Divide each term by 3 and simplify.
Divide each term in 3(x-4)(x+2)=0 by 3.
3(x-4)(x+2)3=03
Simplify 3(x-4)(x+2)3.
Cancel the common factor of 3.
Cancel the common factor.
3(x-4)(x+2)3=03
Divide (x-4)(x+2) by 1.
(x-4)(x+2)=03
(x-4)(x+2)=03
Expand (x-4)(x+2) using the FOIL Method.
Apply the distributive property.
x(x+2)-4(x+2)=03
Apply the distributive property.
x⋅x+x⋅2-4(x+2)=03
Apply the distributive property.
x⋅x+x⋅2-4x-4⋅2=03
x⋅x+x⋅2-4x-4⋅2=03
Simplify and combine like terms.
Simplify each term.
Multiply x by x.
x2+x⋅2-4x-4⋅2=03
Move 2 to the left of x.
x2+2⋅x-4x-4⋅2=03
Multiply -4 by 2.
x2+2x-4x-8=03
x2+2x-4x-8=03
Subtract 4x from 2x.
x2-2x-8=03
x2-2x-8=03
x2-2x-8=03
Divide 0 by 3.
x2-2x-8=0
x2-2x-8=0
Factor x2-2x-8 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 -8 and whose sum is -2.
-4,2
Write the factored form using these integers.
(x-4)(x+2)=0
(x-4)(x+2)=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+2=0
Set the first factor equal to 0 and solve.
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 and solve.
Set the next factor equal to 0.
x+2=0
Subtract 2 from both sides of the equation.
x=-2
x=-2
The final solution is all the values that make (x-4)(x+2)=0 true.
x=4,-2
Solve using the Square Root Property 3x^2+7x-24=13x