What is the solution of sqrt 1 – 3x = x + 3?

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Question:

What is the solution of sqrt 1 – 3x = x + 3?

A. x=-8 or x=-1
B. x=-8
C. x=-1
D. No solution

Answer:

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,

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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!

They would certainly hopefully help the student answer the question by implementing the questions and answer examples. Then could carry out some sharing in a group discussion and also learning with the classmate with regard to the topic, so another student also experience some enlightenment and still keeps up the school learning.

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