# Evaluate square root of 24-5x=x

24-5x=x
To remove the radical on the left side of the equation, square both sides of the equation.
24-5×2=x2
Simplify each side of the equation.
Multiply the exponents in ((24-5x)12)2.
Apply the power rule and multiply exponents, (am)n=amn.
(24-5x)12⋅2=x2
Cancel the common factor of 2.
Cancel the common factor.
(24-5x)12⋅2=x2
Rewrite the expression.
(24-5x)1=x2
(24-5x)1=x2
(24-5x)1=x2
Simplify.
24-5x=x2
24-5x=x2
Solve for x.
Subtract x2 from both sides of the equation.
24-5x-x2=0
Factor the left side of the equation.
Factor -1 out of 24-5x-x2.
Reorder the expression.
Move 24.
-5x-x2+24=0
Reorder -5x and -x2.
-x2-5x+24=0
-x2-5x+24=0
Factor -1 out of -x2.
-(x2)-5x+24=0
Factor -1 out of -5x.
-(x2)-(5x)+24=0
Rewrite 24 as -1(-24).
-(x2)-(5x)-1⋅-24=0
Factor -1 out of -(x2)-(5x).
-(x2+5x)-1⋅-24=0
Factor -1 out of -(x2+5x)-1(-24).
-(x2+5x-24)=0
-(x2+5x-24)=0
Factor.
Factor x2+5x-24 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 -24 and whose sum is 5.
-3,8
Write the factored form using these integers.
-((x-3)(x+8))=0
-((x-3)(x+8))=0
Remove unnecessary parentheses.
-(x-3)(x+8)=0
-(x-3)(x+8)=0
-(x-3)(x+8)=0
Multiply each term in -(x-3)(x+8)=0 by -1
Multiply each term in -(x-3)(x+8)=0 by -1.
(-(x-3)(x+8))⋅-1=0⋅-1
Simplify (-(x-3)(x+8))⋅-1.
Simplify by multiplying through.
Apply the distributive property.
(-x–3)(x+8)⋅-1=0⋅-1
Multiply -1 by -3.
(-x+3)(x+8)⋅-1=0⋅-1
(-x+3)(x+8)⋅-1=0⋅-1
Expand (-x+3)(x+8) using the FOIL Method.
Apply the distributive property.
(-x(x+8)+3(x+8))⋅-1=0⋅-1
Apply the distributive property.
(-x⋅x-x⋅8+3(x+8))⋅-1=0⋅-1
Apply the distributive property.
(-x⋅x-x⋅8+3x+3⋅8)⋅-1=0⋅-1
(-x⋅x-x⋅8+3x+3⋅8)⋅-1=0⋅-1
Simplify and combine like terms.
Simplify each term.
Multiply x by x by adding the exponents.
Move x.
(-(x⋅x)-x⋅8+3x+3⋅8)⋅-1=0⋅-1
Multiply x by x.
(-x2-x⋅8+3x+3⋅8)⋅-1=0⋅-1
(-x2-x⋅8+3x+3⋅8)⋅-1=0⋅-1
Multiply 8 by -1.
(-x2-8x+3x+3⋅8)⋅-1=0⋅-1
Multiply 3 by 8.
(-x2-8x+3x+24)⋅-1=0⋅-1
(-x2-8x+3x+24)⋅-1=0⋅-1
Add -8x and 3x.
(-x2-5x+24)⋅-1=0⋅-1
(-x2-5x+24)⋅-1=0⋅-1
Apply the distributive property.
-x2⋅-1-5x⋅-1+24⋅-1=0⋅-1
Simplify.
Multiply -x2⋅-1.
Multiply -1 by -1.
1×2-5x⋅-1+24⋅-1=0⋅-1
Multiply x2 by 1.
x2-5x⋅-1+24⋅-1=0⋅-1
x2-5x⋅-1+24⋅-1=0⋅-1
Multiply -1 by -5.
x2+5x+24⋅-1=0⋅-1
Multiply 24 by -1.
x2+5x-24=0⋅-1
x2+5x-24=0⋅-1
x2+5x-24=0⋅-1
Multiply 0 by -1.
x2+5x-24=0
x2+5x-24=0
Factor x2+5x-24 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 -24 and whose sum is 5.
-3,8
Write the factored form using these integers.
(x-3)(x+8)=0
(x-3)(x+8)=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-3=0
x+8=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
x-3=0
Add 3 to both sides of the equation.
x=3
x=3
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
x+8=0
Subtract 8 from both sides of the equation.
x=-8
x=-8
The final solution is all the values that make (x-3)(x+8)=0 true.
x=3,-8
x=3,-8
Exclude the solutions that do not make 24-5x=x true.
x=3
Evaluate square root of 24-5x=x

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