Question

Solve each equation by completing the square. X^2=12x+25

Answer 1

The given equation is expressed as

x^2 = 12x + 25

x^2 - 12x = 25

We would add the square of half thecoefficient of x to both sides of the equation

The coefficient of x is - 12

half of the coefficient of x is -6

The square of 6 is - 6^2 = 36

It becomes

x^2 - 12x + (-6)^2 = 25 + 36

(x - 6)^2 = 61

Taking square root of both sides of the equation, it becomes

`\begin{gathered} x-6^{}=+-\sqrt[]{61} \\ x\text{ =}\pm\text{ }\sqrt[]{61}+6 \end{gathered}`