Question

Given the equation −4Square root of x minus 3 = 12, solve for x and identify if it is an extraneous solution.

Answer 1

To solve the provided equation −4√x minus 3 = 12 for x, we isolate the square root, divide both sides by −4, and then square both sides to find that x = 14.0625. We conclude it's not an extraneous solution by substituting it back into the original equation.

Step-by-step explanation:

The original equation provided by the student seems to have a typo and it's not clear. But, if the correct equation is −4√x minus 3 = 12, then we can proceed to solve for x as follows:

1. Isolate the square root: −4√x = 12 + 3
2. Simplify the right side of the equation: −4√x = 15
3. Divide both sides by −4: √x = −3.75
4. Square both sides to eliminate the square root: x = (−3.75)²
5. Calculate the square of −3.75: x = 14.0625

After solving, x = 14.0625 which is our potential solution. We should check if it's not an extraneous solution by substituting it back into the original equation:

−4√(14.0625) − 3 ≠ 12, therefore, the solution x = 14.0625 is not an extraneous solution.

If the equation provided by the student was meant to be a different one and it was a typing error, please provide the correct equation for a precise solution.

Answer 2

There is no solution for the given radical equation.

x = 225/16 is an extraneous solution.

Step-by-step explanation:

The given equation is
`-4\sqrt x-3=12`

Add 3 to both sides of the equation

`-4\sqrt x=15`

Squaring both sides

`16x=225`

Divide both sides by 16

`x=(225)/(16)`

Substituting back the value of x in original equation to check the extraneous solution.

`-4\sqrt ((225)/(16))-3=12\\\\-4\cdot(15)/(4)-3=12\\\\-15-3=12\\\\-18=12`

Since -18≠ 12. Hence, the value of x does not satisfy the equation.

Therefore, x = 225/16 is an extraneous solution.