foass77W
2021-09-20
Answered

Solve the equation.

$\sqrt{3-x}-x=3$

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Sally Cresswell

Answered 2021-09-21
Author has **91** answers

Step 1: Given

$\sqrt{3-x}-x=3$

Step 2: Solution

$\sqrt{3-x}-x=3$

Adding x

$\sqrt{3-x}=3+x$

Squaring both sides

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

${x}^{2}+7x+6=0$

(x+1)(x+6)=0

x+1=0, x+6=0

x=-6, -1

Check

For x=-3

$\sqrt{3--6}--6$

$=3+6=9\ne 3$

Not a solution

For x=−1

$\sqrt{3--1}--1$

$=\sqrt{4}+1$

=2+1

=3

which is same as right side

Answer: x=−1

Step 2: Solution

Adding x

Squaring both sides

(x+1)(x+6)=0

x+1=0, x+6=0

x=-6, -1

Check

For x=-3

Not a solution

For x=−1

=2+1

=3

which is same as right side

Answer: x=−1

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