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The product of two consecutive integers is 72. The equation x(x + 1) = 72 represents the situation, where x represents the smaller integer. Which equation can be factored and solved for the smaller integer? x2 + x – 72 = 0 x2 + x + 72 = 0 x2 + 2x – 72 = 0 x2 + 2x + 72 = 0

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ANSWER

[tex] {x}^{2} + x - 72 = 0[/tex]

EXPLANATION

The given equation is

[tex]x(x + 1) = 72[/tex]

Expand the parenthesis to obtain;

[tex] {x}^{2} + x = 72[/tex]

Add -72 to both sides of the equation.

[tex] {x}^{2} + x - 72 = 0[/tex]

Hence the equation that can be factored and solve for the smaller integer is

[tex] {x}^{2} + x - 72 = 0[/tex]

Answer:

x2 + x – 72 = 0 (option A)

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