Question

question 10 of 10
what would be the most logical first step for solving this quadratic equation?
x² + 2x - 11 = 4
a. take the square root of both sides
b. subtract 4 from both sides
c. add 11 to both sides
d. divide both sides by x

Explanation:

Step1: Recall quadratic - equation form

A quadratic equation is typically in the form $ax^{2}+bx + c=0$. To get the given equation $x^{2}+2x - 11 = 4$ into this standard form, we need to make the right - hand side equal to zero.

Step2: Analyze the options

• Option A: Taking the square root of both sides is not applicable as the left - hand side is not a perfect square and the equation is not in the form $(ax + b)^{2}=c$.
• Option B: Subtracting 4 from both sides gives $x^{2}+2x-11 - 4=4 - 4$, which simplifies to $x^{2}+2x - 15=0$. This puts the equation in the standard quadratic form $ax^{2}+bx + c = 0$ ($a = 1$, $b = 2$, $c=-15$).
• Option C: Adding 11 to both sides gives $x^{2}+2x=15$, which is not the standard quadratic form.
• Option D: Dividing both sides by $x$ is incorrect as it will change the nature of the quadratic equation and may cause us to lose a root (if $x = 0$ was a root, which it isn't in this case, but in general, dividing by a variable is not a valid first step for solving a quadratic).

Answer:

B. Subtract 4 from both sides