Question

consider two consecutive positive integers such that the square of the second integer added to 5 times the first is equal to 19.
step 2 of 2 : find the integers by solving the equation.

Explanation:

Define variables for consecutive integers

Using the Consecutive Integer Word Problems knowledge point
Let the first positive integer be \(n\).
The second consecutive positive integer is \(n + 1\).

Set up the quadratic equation

Using the Consecutive Integer Word Problems knowledge point
The square of the second integer added to 5 times the first is 19:

$$ (n + 1)^2 + 5n = 19 $$

Simplify to standard form

Using the Solving Quadratic Equations knowledge point

$$
LATEXBLOCK0
$$

Solve the quadratic equation

Using the Solving Quadratic Equations knowledge point

$$
LATEXBLOCK1
$$

Determine the positive integers

Using the Consecutive Integer Word Problems knowledge point
Since the problem specifies positive integers:

$$
LATEXBLOCK2
$$

Answer:

Consider two consecutive positive integers such that the square of the second integer added to 5 times the first is equal to 19.
Step 2 of 2 : Find the integers by solving the equation.

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