Question

given the equation x²-6x -10=45, solve the equation by completing the square. be sure to put the correct + or - sign in front of your answer. x²-6x ___ =55 ___(____)²=____so, x-3=____ and x-3=____x=___ and x=___

Answer 1

We are given the following equation

`x^2-6x-10=45`

Let us solve the equation by completing the square method.

Step 1:

Move the constant term (10) to the other side of the equation.

`\begin{gathered} x^2-6x=45+10 \\ x^2-6x=55 \end{gathered}`

Step 2:

Add the square of half of the coefficient of the middle term (that is 6x term) to both sides of the equation

`\begin{gathered} x^2-6x+((6)/(2))^2=55+((6)/(2))^2 \\ x^2-6x+(3)^2=55+(3)^2 \\ x^2-6x+9^{}=55+9 \\ x^2-6x+9=64 \end{gathered}`

Step 3:

The terms on the left side of the equation make a perfect square

`\begin{gathered} x^2-6x+9=64 \\ (x-3)^2=64 \end{gathered}`

Step 4:

To solve for x, take square root on both sides of the equation

`\begin{gathered} \sqrt[]{(x-3)^2}=\sqrt[]{64} \\ x-3=\pm8 \\ x-3=8\quad \text{and}\quad x-3=-8 \\ x=3+8\quad \text{and}\quad x=3-8 \\ x=11\quad \text{and}\quad x=-5 \end{gathered}`

Therefore, the solution of the equation is

`x=11\quad \text{and}\quad x=-5`