Chapter 9.3, Problem 14PPS

To determine

The solutions of the equation $x^2+14x=-49$ by graphing and estimate the roots nearest tenth

Answer to Problem 14PPS

  $x=-7$

Explanation of Solution

Given:

The equation, $x^2+14x=-49$ .

Concept Used:

The solutions of a quadratic equation are given by the points where the graph of the function intersects the x-axis.

In order find the solutions of the given equation $x^2+14x=-49$ , first plot the graph of the function $y=x^2+14x+49$ and identify the zeros of the function.

The zeros of the function are the points where the graph of the function intersects the x-axis.

The graph of the function $y=x^2+14x+49$ is shown below,

  

From the above graph of the function it is clear that the zeros of the function occur at the points $\left(0,49\right),\text{ and }\left(-7,0\right)$ .

Thus, the solution for x is $x=-7$