Answer :
To solve a quadratic equation of the form [tex]\((a x + b)^2 = c\)[/tex], you should follow these steps:
1. Take the square root of both sides: The first step is to eliminate the square on the left-hand side. When you take the square root of both sides of the equation, you get:
[tex]\[ \sqrt{(a x + b)^2} = \sqrt{c} \][/tex]
2. Simplify the equation: Simplifying the left side, you get:
[tex]\[ a x + b = \pm \sqrt{c} \][/tex]
Here, [tex]\(\pm \sqrt{c}\)[/tex] indicates that there are two possible solutions, one for the positive square root and one for the negative square root.
3. Solve for x: Now, you'll solve for [tex]\(x\)[/tex] by isolating it. First, subtract [tex]\(b\)[/tex] from both sides:
[tex]\[ a x = -b \pm \sqrt{c} \][/tex]
4. Divide by a: Finally, divide both sides by [tex]\(a\)[/tex] to isolate [tex]\(x\)[/tex]:
[tex]\[ x = \frac{-b \pm \sqrt{c}}{a} \][/tex]
Given that the first step in this process is to take the square root of both sides, the correct answer is:
D. Take the square root of both sides
1. Take the square root of both sides: The first step is to eliminate the square on the left-hand side. When you take the square root of both sides of the equation, you get:
[tex]\[ \sqrt{(a x + b)^2} = \sqrt{c} \][/tex]
2. Simplify the equation: Simplifying the left side, you get:
[tex]\[ a x + b = \pm \sqrt{c} \][/tex]
Here, [tex]\(\pm \sqrt{c}\)[/tex] indicates that there are two possible solutions, one for the positive square root and one for the negative square root.
3. Solve for x: Now, you'll solve for [tex]\(x\)[/tex] by isolating it. First, subtract [tex]\(b\)[/tex] from both sides:
[tex]\[ a x = -b \pm \sqrt{c} \][/tex]
4. Divide by a: Finally, divide both sides by [tex]\(a\)[/tex] to isolate [tex]\(x\)[/tex]:
[tex]\[ x = \frac{-b \pm \sqrt{c}}{a} \][/tex]
Given that the first step in this process is to take the square root of both sides, the correct answer is:
D. Take the square root of both sides
