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2 years ago

Could someone help me for this?

Mathematics

1 answer:

lina2011 [118]2 years ago

3 0

Answer:

x = - $\frac{5}{3}$ , x = $\frac{5}{2}$

Step-by-step 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 = - $\frac{5}{3}$

2x - 5 = 0 ⇒ 2x = 5 ⇒ x = $\frac{5}{2}$

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