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let m=5x-2.
Which equation is equivalent to (5x-2)^2+35x-14=-12

A. m^2-7m+12=0
B. m^2+7m-2=0
C. m^2-7m-2=0
D. m^2+7m+12=0​

Respuesta :

Answer:

D

Step-by-step explanation:

given

(5x - 2)² + 35x - 14 = - 12 ← factor out 7 from 35x - 14

(5x - 2)² + 7(5x - 2) = - 12 ( add 12 to both sides )

(5x - 2)² + 7(x - 2) + 12 = 0 ← substitute m = 5x - 2, hence

m² + 7m + 12 = 0 → D

The equation is equivalent to [tex]\rm m^2+7m+12=0[/tex].

The correct option is D.

Given

Let m = 5x-2, then the equation is equivalent to (5x-2)^2+35x-14=-12.

How to find an equivalent equation?

To find the equivalent equation solving equation in terms of m.

To find the equivalent equation following all the steps given below.

From equation 1

[tex]\rm m = 5x-2\\\\5x=m+2\\\\x=\dfrac{m+2}{5}[/tex]

Substitute the value of x in equation 2;

[tex]\rm (5x-2)^2+35x-14=-12\\\\\left (5(\dfrac{m+2}{5})-2 \right )^2 + 35(\dfrac{m+2}{5})-14=-12\\\\(m+2-2)^2+7(m+2)-14+12=0\\\\m^2+7m+14-2=0\\\\m^2+7m+12=0[/tex]

Hence, the equation is equivalent to [tex]\rm m^2+7m+12=0[/tex].

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