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2. 4(3x-1)^2=9- solve by taking square root
3. 2x^2-8x+1=0- solve by completing squares
4. 2x^2-3x-20=0- solve by quadratic formula
Simplify and express in a+bi form
5. 2i^74+5i^105
b. (3+i)^2 (1-i)^2
c. i/20+i
solve the equation and express the solution in the form a+bi
6. 4x^2+x+3
b. x^4-16=0
Solve the equation
7. (x+1)^(1/2)=x-5
b. x^4+7x^2-18=0
Solve the inequality in its interval form and graph it
8. / 2x-3/ -4< or = 3 b. x(x-1)^2 (x^2+1)( x-4)>0
/- absolute value
^-power
Someone please help me with these (dont just show the answers show the working so I can understand them, thxs in advance
Favorite Answer
1) 15x^2-11x-14=0
Multiply 15 and -14 to get -210.
Now look at factors or -210 that add up to -11.
The factors are -21 and +10.
Why? Because -21*10 = -210 and -21+10 = -11
Replace -11x with -21x+10x
15x^2 – 21x + 10x – 14 = 0
Factor by grouping the first two terms and grouping the last two terms.
3x(5x-7) + 2(5x-7) = 0
(5x-7)(3x+2) =0
5x-7 = 0 or 3x+2 = 0
x = 7/5 or x = -2/3
2) 4(3x-1)^2=9
Take the square root of each side (remember that when you take the square root of 9, you will get two values (+ or -)).
2(3x-1) = 3 or 2(3x-1) = -3
Solve each equation separately to find the two solutions.
3) 2x^2-8x+1=0
Subtract 1 from each side
2x^2 – 8x = -1
Divide both sides by 2
x^2 – 8x = -1/2
Take the coefficient of x, divide it by 2, then square it. Add this number to both sides.
x^2 – 8x + 16 = -1/2 + 16
(x-4)^2 = 31/2
Now solve by the method of #2.
4) 2x^2-3x-20=0
The quadratic formula says that the solutions of the quadratic equation ax^2 + bx + c = 0 are
x = [-b +/- sqrt(b^2 -4ac)] / (2a)
So a = 2, b = -3, and c = -20.
Plug in those values and simplify.
Last one.
5) 2i^74+5i^105
Let’s look at powers of i.
i^1 = i
i^2 = -1
i^3 = -i
i^4 = 1
i^5 = i
i^6 = -1
i^7 = -i
i^8 = 1
Every four cycles i repeats itself. Also, notice that the power of i is never greater than one. If it is, then that means you can simplify it.
To simplify, divide the exponent by 4 and look at the remainder.
74/4 = 18 remainder 2
That means i^74 = i^2 = -1
105/4 = 26 remainder 1
That means i^105 = i^1 = i
So 2i^74+5i^105
= 2(-1) + 5(i)
= -2 + 5i
