Question

What is the solution of square root 1-3x = x+3

Answer 1

Explanation:

I hope the given equation is :

First step to solve this equation to remove square root from the left side. So, take square on each sides of the equation. Therefore,

1 - 3x = (x + 3)²

1 - 3x = (x + 3)*(x + 3) Since a² = a * a

1 - 3x = x² + 3x + 3x + 3² By multiplication.

1 - 3x = x² + 6x + 9 Combine the like terms.

x² + 6x + 9 - 1 + 3x = 0 Subtract 1 and add 3x from each sides of equation

x² + 9x + 8 = 0 Combine the like terms.

Next step is to factor the trinomial to solve the above equation for x.

For that break downn the constant 8 into two multiples so that the addition of the multiples will result the coefficient of x = 9.

So, 8 = 1 * 8

Addition of 1 and 8 will give 9. So, next step is to replace 9x with 1x + 8x. So,

x² + 1x + 8x + 8 = 0

(x² + 1x) + (8x + 8) = 0 Group the terms.

x ( x + 1) + 8 (x + 1 ) = 0 Take out the common factor from each group.

(x +1 ) ( x + 8 ) = 0 Take out the common factor (x + 1).

So, x + 1 = 0 and x + 8 = 0 Set up each factor equal to 0.

Hence, x = -1 and - 8.

Next step is to plug in -1 and -8 in the original equation to cross check the solutions.

For x = -1,

Simplify each sides separately.

2 = 2

2 = 2 is correct. So, x = -1 satisfy the equation

Hence, x = -1 is the real solution of the given equation.

Similarly let's plug in x = -8 now. So,

Simplify each sides separately.

5 = 2

5 = 2 is not true. So, x = -8 is the extraneous solution.

Therefore, the only solution is x = -1.

Hence, the correct choice is C.

Hope this helps you!

Answer 2

`x = - 1`

EXPLANATION

The given equation is

`√( 1 - 3 x) = x + 3`

Square both sides to get,

`1 - 3x = {(x + 3)}^(2)`

Expand:

`1 - 3x = {x}^(2) + 6x + 9`

`{x}^(2) + 6x + 3x + 9 - 1 = 0`

`{x}^(2) + 9x + 8 = 0`

`{x}^(2) + 8x + x + 8 = 0`

`x(x + 8) + 1(x + 8) = 0`

`(x + 1)(x + 8) = 0`

`x = - 1 \: or \: x = - 8`

Check for extraneous solutions.

When x=-1, we put x=-1 into the original equation:

`√( 1 - 3 ( - 1)) = - 1+ 3`

`√( 1 +3 ) = 2`

`√( 4 ) = 2`

`2 = 2`

This is true.

Also check for x=-8.

`√( 1 - 3 ( - 8)) = - 8+ 3`

`√( 25) = -5`

`5 \\e - 5`

This is an extraneous solution.

Hence x=-1 is the only solution.