WILL GIVE BRAINLIEST: The product of two integers is -144. The sum of the integers is -7. What are the two integers?

The two integers are -16, 9

Step-by-step explanation:

Assume that one of the integers is x

∵ The sum of the integers = -7

∵ One of them = x

∴ The other number = -7 - x

∵ Their product = -144

∴ x(-7 - x) = -144

→ Multiply the bracket by x

∵ x(-7) - x(x) = -144

∴ -7x - x² = -144

→ Multiply all terms by -1

∴ 7x + x² = 144

→ Subtract 144 from both sides

∴ 7x + x² - 144 = 144 - 144

∴ 7x + x² - 144 = 0

→ Arrange the terms of the left side according the greatest power of x

∴ x² + 7x - 144 = 0

→ Let us factorize it into two factors

∵ x × x = x²

∵ 144 = 9 × 16

∵ 16(x) - 9(x) = 7x ⇒ the middle terms

∴ The factors are (x + 16)(x - 9)

∴ x² + 7x - 144 = (x + 16)(x - 9)

→ Equate the factors by 0

∴ (x + 16)(x - 9) = 0

∵ x + 16 = 0

→ Subtract 16 from both sides

∴ x - 16 = 0 - 16

∴ x = -16

∵ The first number is 16

∴ The other number = -7 - (-16) = -7 + 16

∴ The other number = 9

∴ The two integers are -16, 9

You can use the other factor x - 9 = 0, it will give you the same answer