For the following exercise, solve the equation by identifying the quadratic form. Use a substitute variable and find all real solutions by factoring. (x+2)^(2)-25=0

Question

asked Jan 18, 2024 186k views

1 Answer

Floriana · Answer 1 · 2024-01-23T18:00:33+0000

Explanation:

This is a quadratic equation in the form of

vertex form

$(x - h) {}^(2) + k$

where (-2,-25) is the vertex in this case.

$(x + 2) {}^(2) - 25 = 0$

Let u equal x+2

${u}^(2) - 25 = 0$

Use difference of squares and we get

(u - 5)(u + 5) = 0

For the first binomial

u - 5 = 0

u = 5

Remember u=x+2

x + 2 = 5

x = 3

For the Second Binomial, repeat the steps above

x + 2 = - 5

x = - 7

So our solutions are 3 and -7