Answer:
Step-by-step 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
[tex]x = - 1[/tex]
EXPLANATION
The given equation is
[tex] \sqrt{ 1 - 3 x} = x + 3[/tex]
Square both sides to get,
[tex]1 - 3x = {(x + 3)}^{2} [/tex]
Expand:
[tex]1 - 3x = {x}^{2} + 6x + 9[/tex]
[tex] {x}^{2} + 6x + 3x + 9 - 1 = 0[/tex]
[tex] {x}^{2} + 9x + 8 = 0[/tex]
[tex] {x}^{2} + 8x + x + 8 = 0[/tex]
[tex]x(x + 8) + 1(x + 8) = 0[/tex]
[tex](x + 1)(x + 8) = 0[/tex]
[tex]x = - 1 \: or \: x = - 8[/tex]
Check for extraneous solutions.
When x=-1, we put x=-1 into the original equation:
[tex]\sqrt{ 1 - 3 ( - 1)} = - 1+ 3[/tex]
[tex]\sqrt{ 1 +3 } = 2[/tex]
[tex]\sqrt{ 4 } = 2[/tex]
[tex]2 = 2[/tex]
This is true.
Also check for x=-8.
[tex]\sqrt{ 1 - 3 ( - 8)} = - 8+ 3[/tex]
[tex]\sqrt{ 25} = -5[/tex]
[tex]5 \ne - 5[/tex]
This is an extraneous solution.
Hence x=-1 is the only solution.
