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7 August, 06:57

Solve the equation by using quadratic formula X^2+8x=5

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  1. 7 August, 07:13
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    x = sqrt (21) - 4 or x = - sqrt (21) - 4

    Step-by-step explanation by using the quadratic formula:

    Solve for x:

    x^2 + 8 x = 5

    Hint: | Move everything to the left hand side.

    Subtract 5 from both sides:

    x^2 + 8 x - 5 = 0

    Hint: | Using the quadratic formula, solve for x.

    x = (-8 ± sqrt (8^2 - 4 (-5))) / 2 = (-8 ± sqrt (64 + 20)) / 2 = (-8 ± sqrt (84)) / 2:

    x = (-8 + sqrt (84)) / 2 or x = (-8 - sqrt (84)) / 2

    Hint: | Simplify radicals.

    sqrt (84) = sqrt (4*3*7) = sqrt (2^2*3*7) = 2sqrt (3*7) = 2 sqrt (21):

    x = (2 sqrt (21) - 8) / 2 or x = (-2 sqrt (21) - 8) / 2

    Hint: | Factor the greatest common divisor (gcd) of - 8, 2 sqrt (21) and 2 from - 8 + 2 sqrt (21).

    Factor 2 from - 8 + 2 sqrt (21) giving 2 (sqrt (21) - 4):

    x = 1/22 (sqrt (21) - 4) or x = (-2 sqrt (21) - 8) / 2

    Hint: | Cancel common terms in the numerator and denominator.

    (2 (sqrt (21) - 4)) / 2 = sqrt (21) - 4:

    x = sqrt (21) - 4 or x = (-2 sqrt (21) - 8) / 2

    Hint: | Factor the greatest common divisor (gcd) of - 8, - 2 sqrt (21) and 2 from - 8 - 2 sqrt (21).

    Factor 2 from - 8 - 2 sqrt (21) giving 2 (-sqrt (21) - 4):

    x = sqrt (21) - 4 or x = 1/22 (-sqrt (21) - 4)

    Hint: | Cancel common terms in the numerator and denominator.

    (2 (-sqrt (21) - 4)) / 2 = - sqrt (21) - 4:

    Answer: x = sqrt (21) - 4 or x = - sqrt (21) - 4
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