## How many solutions and that type of solutions does the equation (x-7)^2 – 62 = 19 have? Calculate the discriminate to find the answer.

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.

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Math
3 weeks
2021-09-07T00:45:12+00:00
2021-09-07T00:45:12+00:00 1 Answer
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## Answers ( )

Answer:Step-by-step explanation:(a)

For the quadratic equation of the form ,

The discriminant is given as:

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.