Question

question 12 (3 points)
solve each equation by completing the square (put answers in order from least to greatest)
$x^{2}-12x=-20$
the square is $(x+a)^{2}=b$
$a=$
$b=$
which means that $x=$
$\
ightarrow$ or $x=$
blank 1:
blank 2:
blank 3:
blank 4:

Explanation:

Step1: Rewrite the equation

Given \(x^{2}-12x = - 20\).

Step2: Complete the square

For the quadratic \(x^{2}+bx\), the term to add to complete the square is \((\frac{b}{2})^{2}\). Here \(b=-12\), so \((\frac{-12}{2})^{2}=36\).
Add \(36\) to both sides of the equation:
\(x^{2}-12x + 36=-20 + 36\).

Step3: Factor the left - hand side

Using the formula \((a - b)^{2}=a^{2}-2ab + b^{2}\), where \(a = x\) and \(b = 6\), we have \((x - 6)^{2}=16\).
So \(a=-6\) and \(b = 16\).

Step4: Solve for \(x\)

Take the square root of both sides: \(x-6=\pm4\).
If \(x - 6=4\), then \(x=10\).
If \(x - 6=-4\), then \(x = 2\).

Answer:

Blank 1: \(2\), Blank 2: \(10\), Blank 3: \(-6\), Blank 4: \(16\)