Possible intermediate steps:
(3 x-4)^2 = 20-24 x
Expand out terms of the left hand side:
9 x^2-24 x+16 = 20-24 x
Subtract (20-24 x) from both sides:
9 x^2-4 = 0
Add 4 to both sides:
9 x^2 = 4
Divide both sides by 9:
x^2 = 4/9
Take the square root of both sides:
x = -2/3 or x = 2/3
(3 x-4)^2 = 20-24 x
Expand out terms of the left hand side:
9 x^2-24 x+16 = 20-24 x
Subtract (20-24 x) from both sides:
9 x^2-4 = 0
Add 4 to both sides:
9 x^2 = 4
Divide both sides by 9:
x^2 = 4/9
Take the square root of both sides:
x = -2/3 or x = 2/3
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Here is your step by step my friend...
(3x-4)^(2)=20-24x
Since -24x contains the variable to solve for, move it to the left-hand side of the equation by adding 24x to both sides.
(3x-4)^(2)+24x=20
Squaring an expression is the same as multiplying the expression by itself 2 times.
(3x-4)(3x-4)+24x=20
Multiply each term in the first group by each term in the second group using the FOIL method. FOIL stands for First Outer Inner Last, and is a method of multiplying two binomials. First, multiply the first two terms in each binomial group. Next, multiply the outer terms in each group, followed by the inner terms. Finally, multiply the last two terms in each group.
(3x*3x+3x*-4-4*3x-4*-4)+24x=20
Simplify the FOIL expression by multiplying and combining all like terms.
(9x^(2)-24x+16)+24x=20
Since -24x and 24x are like terms, subtract 24x from -24x to get 0.
9x^(2)+16=20
Since 16 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 16 from both sides.
9x^(2)=-16+20
Add 20 to -16 to get 4.
9x^(2)=4
Divide each term in the equation by 9.
(9x^(2))/(9)=(4)/(9)
Simplify the left-hand side of the equation by canceling the common terms.
x^(2)=(4)/(9)
Take the square root of both sides of the equation to eliminate the exponent on the left-hand side.
x=\~((4)/(9))
Pull all perfect square roots out from under the radical. In this case, remove the 2 because it is a perfect square.
x=\(2)/(3)
First, substitute in the + portion of the \ to find the first solution.
x=(2)/(3)
Next, substitute in the - portion of the \ to find the second solution.
x=-(2)/(3)
The complete solution is the result of both the + and - portions of the solution.
x=(2)/(3),-(2)/(3)
(3x-4)^(2)=20-24x
Since -24x contains the variable to solve for, move it to the left-hand side of the equation by adding 24x to both sides.
(3x-4)^(2)+24x=20
Squaring an expression is the same as multiplying the expression by itself 2 times.
(3x-4)(3x-4)+24x=20
Multiply each term in the first group by each term in the second group using the FOIL method. FOIL stands for First Outer Inner Last, and is a method of multiplying two binomials. First, multiply the first two terms in each binomial group. Next, multiply the outer terms in each group, followed by the inner terms. Finally, multiply the last two terms in each group.
(3x*3x+3x*-4-4*3x-4*-4)+24x=20
Simplify the FOIL expression by multiplying and combining all like terms.
(9x^(2)-24x+16)+24x=20
Since -24x and 24x are like terms, subtract 24x from -24x to get 0.
9x^(2)+16=20
Since 16 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 16 from both sides.
9x^(2)=-16+20
Add 20 to -16 to get 4.
9x^(2)=4
Divide each term in the equation by 9.
(9x^(2))/(9)=(4)/(9)
Simplify the left-hand side of the equation by canceling the common terms.
x^(2)=(4)/(9)
Take the square root of both sides of the equation to eliminate the exponent on the left-hand side.
x=\~((4)/(9))
Pull all perfect square roots out from under the radical. In this case, remove the 2 because it is a perfect square.
x=\(2)/(3)
First, substitute in the + portion of the \ to find the first solution.
x=(2)/(3)
Next, substitute in the - portion of the \ to find the second solution.
x=-(2)/(3)
The complete solution is the result of both the + and - portions of the solution.
x=(2)/(3),-(2)/(3)
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(3*-4)^2=20-24x
(-12)^2=20-24x
-24=20-24x
I spent 20 min doing this i got stuck here.
(-12)^2=20-24x
-24=20-24x
I spent 20 min doing this i got stuck here.
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9x^2-24x+16=20-24x
(get rid of the 24x)
9x^2=20-16
9x^2=4
4/9=0.4444444444444^-0.5
x=2/3
(get rid of the 24x)
9x^2=20-16
9x^2=4
4/9=0.4444444444444^-0.5
x=2/3