Question

How many solutions and that type of solutions does the equation (x-7)^2 - 62 = 19 have? Calculate the discriminate to find the answer.
Solve the equation (x-7)^2 - 62 = 19. Show your work and explain your steps. If you do not explain or show your work, you will not receive credit.

Answer 1

Answer:

Step-by-step explanation:

(a)

For the quadratic equation of the form $ax^{2} +bx+c=0$,

The discriminant is given as: $b^{2} - 4ac$

Simplifying the given quadratic equation:

[(x-7)^2] - 62 = 19

∴ (x^2) - 14x + 49 = 81

∴ (x^2) - 14x - 32 = 0

Comparing with the standard form of quadratic equation:

a = 1; b = -14; c = -32

∴ Discriminant = (b^2) - 4ac = 196 + 128 = 324

Since Discriminant > 0,

The roots will be real and distinct.

(b)

This equation can be factored as:

(x - 16)(x + 2) = 0;

∴ x = 16 ; x = -2, are the two roots of the equation.