In simplest radical form, what are the solutions to the quadratic equation 0 = –3x2 – 4x + 5? Quadratic formula: x = StartFracti
2 answers:
The solutions of the quadratic equation 0 = -3x² - 4x + 5 are
and
Step-by-step explanation:
The quadratic formula of the quadratic equation ax² + bx + c = 0, is
To find the solution of the quadratic equation by using quadratic formula
- Find the values of a, b, and c from the quadratic equation
- Substitute these values in the quadratic formula
- Calculate the values of x
∵ -3x² - 4x + 5 = 0
∴ a = -3 , b = -4 and c = 5
- Substitute these values in the quadratic formula
∵
∴
∴
- Simplify by dividing up and down by -2
∴
∵
∴
∴
- Simplify by dividing up and down by -2
∴
The solutions of the quadratic equation 0 = -3x² - 4x + 5 are
and
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These are a huge pain. First set up your initial triangle with A and B as your base angles and C as your vertex angle. Now drop an altitude and call it h. You need to solve for h. Use sin 56 = h/13 to get that h = 10.8. The rule is that if the side length of a is greater than the height but less than the side length of b, you have 2 triangles. h<a<b --> 10.8<12<13. Those are true statements so we have 2 triangles. Side a is the side that swings, this is the one we "move", forming the second triangle. First we have to solve the first triangle using the Law of Sines, then we can solve the second. 
to get that angle B is 64 degrees. Now find C: 180-56-64=60. And now for side c: 
and c=12.5. That's your first triangle. In the second triangle, side a is the swinging side and that length doesn't change. Neither does the angle measure. Angle B has a supplement of 180-64 which is 116. So the new angle B in the second triangle is 116, but the length of b doesn't change, either. I'll show you how you know you're right about that in just a sec. The only angle AND side that both change are C and c. If our new triangle has angles 56 and 116, then C has to be 8 degrees. Using the Law of Sines again, we can solve for c:
and c = 2.0. We can look at this new triangle and determine the side measures are correct because the longest side will always be across from the largest angle, and the shortest side will always be across from the smallest angle. The new angle B is 116, which is across from the longest side of 13. These are hard. Ugh.
Answer:
The solution for is all real numbers less that or equal to 36.
Step-by-step explanation:
Given expression:
To find the solution for
Solution:
In order to solve for , we will make sure to isolate the unknown variable
on left side alone by doing math operations on both sides of the inequality.
We have:
Multiplying both sides by 2.
The 2 on left side will cancel each other leaving alone.
Thus, we have:
Thus, solution for is all real numbers less that or equal to 36.