Question

Solve the quadratic equation by completing the square: x² – 10 + 16 = 0

Answer 1

x = 8 or x = 2

Step-by-step explanation:

Given the below quadratic equation;

`x^2-10x+16=0`

To solve the above using the completing the squares method, we'll have to follow the below-outlined steps;

1. Subtract 16 from both sides of the equation;

`\begin{gathered} x^2-10x+16-16=0-16 \\ x^2-10x=-16 \end{gathered}`

2. Add 1/2 of the coefficient of x squared to both sides of the equation;

`\begin{gathered} x^2-10x+((-10)/(2))^2=-16+((-10)/(2))^2 \\ x^2-10x+25=-16+25 \\ x^2-10x+25=9 \end{gathered}`

3. Factor the left-hand side of the equation into a perfect square;

`(x-5)^2=9`

4. Let's go ahead and take the square root of both sides and solve for x;

`\begin{gathered} x-5=\sqrt[]{9} \\ x-5=3 \\ x=8 \\ Or \\ x-5=-3 \\ x=5-3 \\ x=2 \end{gathered}`