Question

Find the equation that results from completing the square in the following equation.

Answer 1

➢ Answєr :

$\Huge{\boxed{\sf{\orange{ {(x - 6)}^2 =25}}}}$

➢ Explαnαtion :

$\displaystyle{\sf{{x}^2 - 12x + 11 = 0}}$

Subtract 11 from both the sides.

$\displaystyle{\sf{{x}^2 - 12x + 11 - 11 = 0 - 11}}$

$\implies$$\displaystyle{\sf{{x}^2 - 12x = - 11}}$

To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of b

$\displaystyle{\sf{{( \frac{b}{2})}^2 = -6}}$

Add the term to each side of the equation.

$\implies$$\displaystyle{\sf{{x}^2 - 12x {-6}^2 = - 11 {-6}^2}}$

Simplify the equation.

$\implies$$\displaystyle{\sf{{x}^2 - 12x + 36 = 25}}$

Factor the perfect trinomial square into $\displaystyle{\sf{(x-6)^2 }}$

$\large{\boxed{\sf{\red{(x-6)^2 = 25}}}}$

Answer 2

$\text{Hello there! :)}$

$\large\boxed{ (x-6)^{2} =25}$

$x^{2} - 12x + 11 = 0\\\\\text{Complete the square by creating a perfect square trinomial:}\\\\ \text{Move 11 to the other side:}\\\\x^{2} - 12x = -11\\\text{Divide the second term by 2 and square to complete the square.}\\\\\text{Make sure to add 36 to both sides:}\\x^2 - 12x + (36) = -11 + (36)\\\\\text{Simplify:}\\\\(x - 6)^{2} = -11 + 36 \\\\(x-6)^{2} = 25$