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How do you solve the equation: #x^2 + 7x - 3 = 0#?

Answer 1

Isaiah Anthony

The solutions are:
#x = color(blue)( (-7+sqrt(61))/(2 #

# x =color(blue)( (-7-sqrt(61))/(2#

#x^2+7x-3=0#

The equation is of the form #color(blue)(ax^2+bx+c=0# where: #a=1, b=7, c=-3#

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

# = (7)^2-(4*(1)*(-3)#

# = 49 +12=61#

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

#x = ((-7)+-sqrt(61))/(2*1) = ((-7)+-sqrt(61))/(2# The solutions are: #x = color(blue)( (-7+sqrt(61))/(2 #

# x =color(blue)( (-7-sqrt(61))/(2#

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Answer 2

Eva Adamson

To solve the equation x^2 + 7x - 3 = 0, you can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

where a = 1, b = 7, and c = -3.

Substitute these values into the quadratic formula:

x = (-7 ± √(7^2 - 4(1)(-3))) / (2(1))

Calculate the discriminant:

b^2 - 4ac = 7^2 - 4(1)(-3) = 49 + 12 = 61

Now, substitute the discriminant back into the formula:

x = (-7 ± √61) / 2

So, the solutions are:

x = (-7 + √61) / 2 and x = (-7 - √61) / 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.