Question

one positive number is 5 more than twice another. their product is 52.
step 2 of 2: find the numbers by solving the equation.

Explanation:

Translate the word problem to an equation

Using the Translating Word Problems to Quadratic Equations knowledge point
Let \(x\) be the smaller positive number.
The other positive number is \(2x + 5\).
Their product is 52:

$$ x(2x + 5) = 52 $$

Write the quadratic equation in standard form

Using the Standard Form of Quadratic Equations knowledge point

$$ 2x^2 + 5x - 52 = 0 $$

Solve the quadratic equation by factoring

Using the Factoring Quadratic Equations and Solving Quadratic Equations knowledge points

$$
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$$

Find the positive numbers

Using the Zero Product Property knowledge point

$$
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$$

Answer:

One positive number is 5 more than twice another. Their product is 52.
Step 2 of 2 : Find the numbers by solving the equation.
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