Question

one number is 34 more than another. their product is -289.

step 2 of 2 : find the numbers by solving the equation.

Explanation:

Define variables and set up the equation

Let the smaller number be \(x\).
The other number is \(34\) more than \(x\), which is \(x + 34\).
Their product is given as \(-289\).
We write the equation:

$$x(x + 34) = -289$$

Write the quadratic equation in standard form

Using the Solving Quadratic Equations knowledge point

$$
LATEXBLOCK0
$$

Factor the quadratic equation

Using the Square of a Binomial Sum knowledge point

$$
LATEXBLOCK1
$$

Solve for x

Using the Solving Quadratic Equations knowledge point

$$
LATEXBLOCK2
$$

Find the two numbers

The first number is \(x = -17\).
The second number is:

$$x + 34 = -17 + 34 = 17$$

The two numbers are \(-17\) and \(17\).

Answer:

\(-17\) and \(17\)