How do you solve #3x^2+14x+15=0#?

Answer 1

#x = -5/3# or #x = -3#

#=> 3x^2 + 14x + 15 = 0#
It’s in the form of #ax^2 + bx + c = 0#

where,

Use formula for quadratic equation to find #x#
#x = (-b +- sqrt(b^2 - 4ac))/(2a)#
#x = (-14 +- sqrt(14^2 - (4 × 3 × 15)))/(2 × 3)#
#x = (-14 +- sqrt(196 - 180))/(6)#
#x = (-14 +- sqrt(16))/6#
#x = (-14 +-4)/6#
#x = (-14 + 4)/6 color(white)(....) "or" color(white)(....) x = (-14 - 4)/6#
#x = (-10)/6 color(white)(..........) "or" color(white)(....) x = (-18)/6#
#x = -5/3 color(white)(..........) "or" color(white)(....)x = -3#
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Answer 2

I would use the quadratic formula.

Equations of the following type can be solved using the quadratic formula:

#ax^2+bx+c=0#

And appears as follows:

#x= (-b+- sqrt(b^2-4ac))/(2a)#

In our instance:

#a=3# #b=14# #c=15#
#x= (-14+- sqrt((14)^2-4(3)(15)))/((2)(3))#
#x= (-14+- sqrt(196-180))/(6)#
#x= (-14+- sqrt(16))/(6)#
#x= (-14+- 4)/(6)#

So:

#x_1=(-18/6)=-3#
#x_2=(-10/6)=-5/3#
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Answer 3

To solve the quadratic equation 3x^2 + 14x + 15 = 0, you can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a), where a = 3, b = 14, and c = 15. Plugging in these values, you get x = (-14 ± √(14^2 - 4(3)(15))) / (2*3). Simplifying further, you get x = (-14 ± √(196 - 180)) / 6, which becomes x = (-14 ± √16) / 6. This simplifies to x = (-14 ± 4) / 6. Therefore, the solutions are x = (-14 + 4) / 6 = -10 / 6 = -5/3 and x = (-14 - 4) / 6 = -18 / 6 = -3. So, the solutions are x = -5/3 and x = -3.

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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.

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.

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.

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.

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