Answer:
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
