Question

question 6 of 10
what is the most logical first step in solving the equation
$x^2 + 14x + 49 = 19$
a. factor the left side of the equation
b. take the square root of both sides of the equation
c. subtract 49 from both sides of the equation
d. subtract 19 from both sides of the equation

Explanation:

The left - hand side of the equation \(x^{2}+14x + 49\) is a perfect square trinomial. A perfect square trinomial of the form \(a^{2}+2ab + b^{2}=(a + b)^{2}\). In the expression \(x^{2}+14x + 49\), we have \(a=x\), \(2ab = 14x\) (so \(b = 7\) since \(2\times x\times7=14x\)) and \(b^{2}=49\). So \(x^{2}+14x + 49=(x + 7)^{2}\). The most logical first step to solve the equation \(x^{2}+14x + 49=19\) is to factor the left - hand side. If we take the square root of both sides first, the left - hand side is not in a simple square form yet (before factoring). Subtracting 49 or 19 from both sides is not the most logical first step as factoring the perfect square trinomial simplifies the equation for further steps (like taking the square root after factoring).

Answer:

A. Factor the left side of the equation