# Solve for c c-2 square root of 9-c=9 c-29-c=9
Subtract c from both sides of the equation.
-29-c=9-c
Divide each term by -2 and simplify.
Divide each term in -29-c=9-c by -2.
-29-c-2=9-2+-c-2
Cancel the common factor of -2.
Cancel the common factor.
-29-c-2=9-2+-c-2
Divide 9-c by 1.
9-c=9-2+-c-2
9-c=9-2+-c-2
Simplify each term.
Move the negative in front of the fraction.
9-c=-92+-c-2
Dividing two negative values results in a positive value.
9-c=-92+c2
9-c=-92+c2
9-c=-92+c2
To remove the radical on the left side of the equation, square both sides of the equation.
9-c2=(-92+c2)2
Simplify each side of the equation.
Multiply the exponents in ((9-c)12)2.
Apply the power rule and multiply exponents, (am)n=amn.
(9-c)12⋅2=(-92+c2)2
Cancel the common factor of 2.
Cancel the common factor.
(9-c)12⋅2=(-92+c2)2
Rewrite the expression.
(9-c)1=(-92+c2)2
(9-c)1=(-92+c2)2
(9-c)1=(-92+c2)2
Simplify.
9-c=(-92+c2)2
9-c=(-92+c2)2
Solve for c.
Simplify (-92+c2)2.
Rewrite (-92+c2)2 as (-92+c2)(-92+c2).
9-c=(-92+c2)(-92+c2)
Expand (-92+c2)(-92+c2) using the FOIL Method.
Apply the distributive property.
9-c=-92(-92+c2)+c2(-92+c2)
Apply the distributive property.
9-c=-92(-92)-92⋅c2+c2(-92+c2)
Apply the distributive property.
9-c=-92(-92)-92⋅c2+c2(-92)+c2⋅c2
9-c=-92(-92)-92⋅c2+c2(-92)+c2⋅c2
Simplify and combine like terms.
Simplify each term.
Multiply -92(-92).
Multiply -1 by -1.
9-c=1(92)92-92⋅c2+c2(-92)+c2⋅c2
Multiply 92 by 1.
9-c=92⋅92-92⋅c2+c2(-92)+c2⋅c2
Multiply 92 and 92.
9-c=9⋅92⋅2-92⋅c2+c2(-92)+c2⋅c2
Multiply 9 by 9.
9-c=812⋅2-92⋅c2+c2(-92)+c2⋅c2
Multiply 2 by 2.
9-c=814-92⋅c2+c2(-92)+c2⋅c2
9-c=814-92⋅c2+c2(-92)+c2⋅c2
Multiply -92⋅c2.
Multiply c2 and 92.
9-c=814-c⋅92⋅2+c2(-92)+c2⋅c2
Multiply 2 by 2.
9-c=814-c⋅94+c2(-92)+c2⋅c2
9-c=814-c⋅94+c2(-92)+c2⋅c2
Move 9 to the left of c.
9-c=814-9⋅c4+c2(-92)+c2⋅c2
Multiply c2(-92).
Multiply c2 and 92.
9-c=814-9c4-c⋅92⋅2+c2⋅c2
Multiply 2 by 2.
9-c=814-9c4-c⋅94+c2⋅c2
9-c=814-9c4-c⋅94+c2⋅c2
Move 9 to the left of c.
9-c=814-9c4-9⋅c4+c2⋅c2
Multiply c2⋅c2.
Multiply c2 and c2.
9-c=814-9c4-9c4+c⋅c2⋅2
Raise c to the power of 1.
9-c=814-9c4-9c4+c1c2⋅2
Raise c to the power of 1.
9-c=814-9c4-9c4+c1c12⋅2
Use the power rule aman=am+n to combine exponents.
9-c=814-9c4-9c4+c1+12⋅2
Add 1 and 1.
9-c=814-9c4-9c4+c22⋅2
Multiply 2 by 2.
9-c=814-9c4-9c4+c24
9-c=814-9c4-9c4+c24
9-c=814-9c4-9c4+c24
Subtract 9c4 from -9c4.
9-c=814-29c4+c24
9-c=814-29c4+c24
Simplify each term.
Cancel the common factor of 2.
Factor 2 out of -2.
9-c=814+2(-1)9c4+c24
Factor 2 out of 4.
9-c=814+2⋅-19c2⋅2+c24
Cancel the common factor.
9-c=814+2⋅-19c2⋅2+c24
Rewrite the expression.
9-c=814-19c2+c24
9-c=814-19c2+c24
Rewrite -19c2 as -9c2.
9-c=814-9c2+c24
9-c=814-9c2+c24
9-c=814-9c2+c24
Since c is on the right side of the equation, switch the sides so it is on the left side of the equation.
814-9c2+c24=9-c
Move all terms containing c to the left side of the equation.
Add c to both sides of the equation.
814-9c2+c24+c=9
To write c as a fraction with a common denominator, multiply by 22.
814+c24-9c2+c⋅22=9
Combine c and 22.
814+c24-9c2+c⋅22=9
Combine the numerators over the common denominator.
814+c24+-9c+c⋅22=9
Add -9c and c⋅2.
Reorder c and 2.
814+c24+-9c+2⋅c2=9
Add -9c and 2⋅c.
814+c24+-7c2=9
814+c24+-7c2=9
Move the negative in front of the fraction.
814+c24-7c2=9
814+c24-7c2=9
Multiply each term by 4 and simplify.
Multiply each term in 814+c24-7c2=9 by 4.
814⋅4+c24⋅4-7c2⋅4=9⋅4
Simplify each term.
Cancel the common factor of 4.
Cancel the common factor.
814⋅4+c24⋅4-7c2⋅4=9⋅4
Rewrite the expression.
81+c24⋅4-7c2⋅4=9⋅4
81+c24⋅4-7c2⋅4=9⋅4
Cancel the common factor of 4.
Cancel the common factor.
81+c24⋅4-7c2⋅4=9⋅4
Rewrite the expression.
81+c2-7c2⋅4=9⋅4
81+c2-7c2⋅4=9⋅4
Cancel the common factor of 2.
Move the leading negative in -7c2 into the numerator.
81+c2+-7c2⋅4=9⋅4
Factor 2 out of 4.
81+c2+-7c2⋅(2(2))=9⋅4
Cancel the common factor.
81+c2+-7c2⋅(2⋅2)=9⋅4
Rewrite the expression.
81+c2-7c⋅2=9⋅4
81+c2-7c⋅2=9⋅4
Multiply 2 by -7.
81+c2-14c=9⋅4
81+c2-14c=9⋅4
Multiply 9 by 4.
81+c2-14c=36
81+c2-14c=36
Move 36 to the left side of the equation by subtracting it from both sides.
81+c2-14c-36=0
Subtract 36 from 81.
c2-14c+45=0
Factor c2-14c+45 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 45 and whose sum is -14.
-9,-5
Write the factored form using these integers.
(c-9)(c-5)=0
(c-9)(c-5)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
c-9=0
c-5=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
c-9=0
Add 9 to both sides of the equation.
c=9
c=9
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
c-5=0
Add 5 to both sides of the equation.
c=5
c=5
The final solution is all the values that make (c-9)(c-5)=0 true.
c=9,5
c=9,5
Exclude the solutions that do not make c-29-c=9 true.
c=9
Solve for c c-2 square root of 9-c=9

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