Question

Solve the equation by completing the square.x^2-10x+26=8Fill in the values of a and b to complete the solutions.Vo0x=a-√√bx=a+√ √b=< >

Answer 1

Given the equation:

`x^2-10x+26=8`

Let's find the solution using the quadratic formula.

Equate to zero by subtracting x from both sides of the equation:

`\begin{gathered} x^2-10x+26-8=8-8 \\ \\ x^2-10x+18=0 \end{gathered}`

Apply the quadratic formula:

`x=(-b\pm√(b^2-4ac))/(2a)`

Where:

a = 1

b = -10

c = 18

Plug in the values in the equation and solve for x.

We have:

`\begin{gathered} x=(--10\pm√(-10^2-4(1)(18)))/(2(1)) \\ \\ x=(10\pm√(100-72))/(2) \\ \\ x=(10\pm√(28))/(2) \end{gathered}`

Solving further:

`\begin{gathered} x=(10+√(7*4))/(2) \\ \\ x=(10+√(7*2^2))/(2) \\ \\ x=(10+2√(7))/(2) \\ \\ x=(10)/(2)\pm(2√(7))/(2) \\ \\ x=5\pm√(7) \\ \\ x=5-√(7) \\ x=5+√(7) \end{gathered}`

Therefore, the values of a and b are:

a = 5

b = 7

• ANSWER:

a = 5

b = 7