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:

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Where:

a = 1

b = -10

c = 18

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

We have:

$\begin{gathered} x=\frac{--10\pm\sqrt{-10^2-4(1)(18)}}{2(1)} \\ \\ x=\frac{10\pm\sqrt{100-72}}{2} \\ \\ x=\frac{10\pm\sqrt{28}}{2} \end{gathered}$

Solving further:

$\begin{gathered} x=\frac{10+\sqrt{7*4}}{2} \\ \\ x=\frac{10+\sqrt{7*2^2}}{2} \\ \\ x=\frac{10+2\sqrt{7}}{2} \\ \\ x=\frac{10}{2}\pm\frac{2\sqrt{7}}{2} \\ \\ x=5\pm\sqrt{7} \\ \\ x=5-\sqrt{7} \\ x=5+\sqrt{7} \end{gathered}$

Therefore, the values of a and b are:

a = 5

b = 7

• ANSWER:

a = 5

b = 7