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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Madelyn 3 weeks 2021-09-07T00:45:12+00:00 1 Answer 0

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    2021-09-07T00:46:32+00:00

    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.

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