QuestionThe length of a rectangle is 7 yd more than twice the width $x$. The area is $490 \mathrm{yd}^{2}$.
Part: 0 / 3 $\square$
Part 1 of 3 (a) Write an equation in terms of $x$ that represents the given relationship.
The equation is $\square$ . $\square$

Studdy Solution
Simplify the equation to obtain a quadratic equation in terms of $x$.
Distribute $x$ on the right-hand side: $$490 = x(2x + 7)$$ $$490 = 2x^2 + 7x$$ Rearrange to form a standard quadratic equation: $$2x^2 + 7x - 490 = 0$$
The equation representing the given relationship is: $$2x^2 + 7x - 490 = 0$$