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How do you solve # y = x^2 − 8x + 7# using the quadratic formula?

Answer 1

Eva Adamson

The solutions for the quadratic equation are:
#color(blue)(x=7#
#color(blue)(x=1#

#y = x^2 -8x + 7#

The equation is of the form #color(blue)(ax^2+bx+c=0# where: #a=1, b=-8, c=7#

The Discriminant is given by: #Delta=b^2-4*a*c#

# = (-8)^2-(4 * 1 * 7)#

# = 64 -28 =36#

The solutions are found using the formula #x=(-b+-sqrtDelta)/(2*a)#

#x = (-(-8)+-sqrt(36))/(2*1) = (8+-6)/2#

#x = ( 8 + 6) /2 = 14/2 = 7#

#x = ( 8 - 6) /2 = 2/2 = 1#

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Answer 2

Ethan Adkins

To solve the quadratic equation (y = x^2 - 8x + 7) using the quadratic formula, you can use the formula:

[ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} ]

where ( a = 1 ), ( b = -8 ), and ( c = 7 ).

Substituting these values into the formula:

[ x = \frac{{-(-8) \pm \sqrt{{(-8)^2 - 4(1)(7)}}}}{{2(1)}} ]

[ x = \frac{{8 \pm \sqrt{{64 - 28}}}}{{2}} ]

[ x = \frac{{8 \pm \sqrt{{36}}}}{{2}} ]

Thus, the solutions are:

[ x = \frac{{8 + \sqrt{{36}}}}{{2}} ] or [ x = \frac{{8 - \sqrt{{36}}}}{{2}} ]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.