x-sqrt(2x+1) = 7
My answer:
same as:
x - 7 = sqrt(2x+1)
==>
x^2 - 14x + 49 = 2x+1 ==>
x^2 - 16x + 48 = 0
split this up into:
(x - 12) * ( x - 4 ) = 0
so, x can technically be 12 or 4
12 - sqrt(24+1) does = 7
x=12
wrong...
x^2 times (2x+1 )
equals 2x^3 + 2x^2 -7 =0
ohhh I'm so sorry. I misread the question...but your answer is still wrong
you would square both sides by 2
and then and up w/ 2x+1 = 49
What about the x?
Maria, you are correct
x = 12 is the right answer, since x= 4 does not verify when you try it back in the original.
To solve the equation x - sqrt(2x+1) = 7, you can follow these steps:
Step 1: Start by isolating the square root term by subtracting 7 from both sides of the equation:
x - sqrt(2x+1) - 7 = 0
Step 2: Move the square root term to the other side of the equation:
x - 7 = sqrt(2x+1)
Step 3: Square both sides of the equation to eliminate the square root:
(x - 7)^2 = (sqrt(2x+1))^2
x^2 - 14x + 49 = 2x + 1
Step 4: Simplify the equation by combining like terms:
x^2 - 16x + 48 = 0
Step 5: Factor the quadratic equation:
(x - 12)(x - 4) = 0
Step 6: Set each factor equal to zero and solve for x:
x - 12 = 0 or x - 4 = 0
Solving the first equation:
x = 12
Solving the second equation:
x = 4
Therefore, x can either be 12 or 4.
And to check which value satisfies the original equation, substitute x = 12:
12 - sqrt(2(12) + 1) = 7
12 - sqrt(24 + 1) = 7
12 - sqrt(25) = 7
12 - 5 = 7
7 = 7
So, x = 12 is the solution to the equation x - sqrt(2x+1) = 7.