24-5x=x

To remove the radical on the left side of the equation, square both sides of the equation.

24-5×2=x2

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

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