The square of a positive number is 21 more than 4 times the number. How do you find the number?

Apr 14, 2018

$x = 7$

Explanation:

First, translate the statement into an equation:

${x}^{2} = 21 + 4 x \text{ }$ Subtract 21 and 4x on both sides to get:

${x}^{2} - 4 x - 21 = 0 \text{ }$ Factor the quadratic to get:

$\left(x - 7\right) \left(x + 3\right) = 0 \text{ }$ Set each factor equal to zero:

$x - 7 = 0$ and $x + 3 = 0 \text{ }$ Solve each equation:

$x = 7$ and $x = - 3$

Since the statement said it must be a "positive" number, we go with only 7.