Question

question solve the equation for all values of x by completing the square. express your answer in simplest form. $x^{2}-2x = 48$ answer attempt 1 out of 2 + additional solution - no solution $x=$

Explanation:

Step1: Add square of half - coefficient of x.

The coefficient of $x$ is $- 2$. Half of it is $-1$, and its square is $1$. Add $1$ to both sides of the equation $x^{2}-2x = 48$. So we get $x^{2}-2x + 1=48 + 1$.

Step2: Rewrite left - hand side as square.

The left - hand side $x^{2}-2x + 1$ can be written as $(x - 1)^{2}$ according to the perfect - square formula $(a - b)^2=a^{2}-2ab + b^{2}$. So, $(x - 1)^{2}=49$.

Step3: Take square root of both sides.

Taking the square root of both sides gives $x-1=\pm\sqrt{49}=\pm7$.

Step4: Solve for x.

For $x - 1 = 7$, we get $x=7 + 1=8$. For $x - 1=-7$, we get $x=-7 + 1=-6$.

Answer:

$x = 8$ or $x=-6$