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Could someone help me for this?

Could someone help me for this?-example-1
User Jclancy
by
2.6k points

1 Answer

25 votes
25 votes

Answer:

x = -
(5)/(3) , x =
(5)/(2)

Explanation:

to find the points of intersection equate the 2 equations , that is

7x - 15 = 10 + 12x - 6x² ( subtract 10 + 12x - 6x² from both sides )

6x² - 5x - 25 = 0 ← factor the quadratic on left side

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 6 × - 25 = - 150 and sum = - 5

the factors are - 15 and + 10

use these factors to split the x- term

6x² - 15x + 10x - 25 = 0 ( factor the first/second and third/fourth terms )

3x(2x - 5) + 5(2x - 5) = 0 ← factor out (2x - 5) from each term

(2x - 5)(3x + 5) = 0

equate each factor to zero and solve for x

3x + 5 = 0 ⇒ 3x = - 5 ⇒ x = -
(5)/(3)

2x - 5 = 0 ⇒ 2x = 5 ⇒ x =
(5)/(2)

User Ruwan
by
2.9k points