Solve the following equation.
16x-8square roots of x = 35
It would be 16 * 35 = 560 - 8 = 552..
Am I reading it right.. 16(x) - 8
x = 35
Is 8 an exponent?
I'm sorry...
(16x)- 8square roots of x = 35
16x - 8√x = 35
16x - 8√x - 35 = 0
(4√x + 5)(4√x - 7) = 0
. . .
To solve the equation, we need to isolate the variable x. Let's go through the steps:
1. Start by moving the constant term (35) to the other side of the equation.
16x - 8√x = 35 becomes 16x - 8√x - 35 = 0
2. Next, let's combine like terms. We have two terms with x and a single term with the square root of x.
16x - 8√x - 35 = 0 can be rewritten as (16x - 8√x) - 35 = 0
3. Now, we want to isolate the term with the square root of x. Move the constant (-35) to the right side of the equation.
(16x - 8√x) - 35 = 0 becomes 16x - 8√x = 35
4. To eliminate the square root, we'll square both sides of the equation.
(16x - 8√x)^2 = 35^2
Squaring the left side of the equation will require expanding the expression (16x - 8√x)^2.
(16x - 8√x)^2 = 256x^2 - 256x√x + 64x
Simplifying the right side of the equation:
256x^2 - 256x√x + 64x = 1225
5. Rearrange the terms to bring them all to one side of the equation:
256x^2 - 256x√x + 64x - 1225 = 0
Now, we have a quadratic equation in terms of x (√x) that we can solve using various methods such as factoring, completing the square, or using the quadratic formula. Let's continue the process by factoring:
6. Factor the quadratic equation.
(16x - 25)(16x - 49) = 0
Now, we set each factor equal to zero and solve for x:
For the first factor: 16x - 25 = 0
16x = 25
x = 25/16
For the second factor: 16x - 49 = 0
16x = 49
x = 49/16
So, the solutions to the original equation are x = 25/16 and x = 49/16.