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kherson [118]
3 years ago
8

Using the quadratic formula to solve 4x2 – 3x + 9 = 2x + 1, what are the values of x?

Mathematics
2 answers:
yaroslaw [1]3 years ago
8 0

Answer:

The value of x is:

x=\dfrac{5\pm \sqrt{103}i}{8}

Step-by-step explanation:

we have to use the quadratic formula to solve for x.

The equation is given as:

4x^2-3x+9=2x+1

which could also be written as:

4x^2-3x+9-2x-1=0\\\\4x^2-3x-2x+9-1=0\\\\\\4x^2-5x+8=0

The quadratic formula for the quadratic equation of the type:

ax^2+bx+c=0 is given as:

x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}

Here we have:

a=4, b=-5 and c=8.

Hence, by the quadratic formula we have:

x=\dfrac{-(-5)\pm \sqrt{(-5)^2-4\times 8\times 4}}{2\times 4}\\\\x=\dfrac{5\pm \sqrt{25-128}}{8}\\\\\\x=\dfrac{5\pm \sqrt{103}i}{8}

Hence, the value of x is:

x=\dfrac{5\pm \sqrt{103}i}{8}

noname [10]3 years ago
8 0

Answer:

Choice c is the answer.

Step-by-step explanation:

We have given a quadratic equation.

4x²-3x+9 = 2x+1

We have to solve above equation using quadratic formula.

First , Add -2x-1 into both sides of given equation, we have

4x²-3x+9 -2x-1 = 2x+1 -2x-1

Adding like terms, we have

4x²-5x+8  = 0 is general form of quadratic equation, where a = 4, b = -5 and c= 8.

x = (-b±√b²-4ac) / 2a is quadratic formula.

Putting given values in above equation, we have

x = (-(-5)±√(-5)²-4(4)(8) ) / 2(4)

x = (5±√24-128) / 8

x = (5±√-103) / 8

x = (5±√103√-1) / 8          ∴√-1 = i

x = (5±√103i) / 8 Which is the answer.

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Answer:

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Step-by-step explanation:

1) The best option is to break down this triangle. Let's draw an altitude from Point B down to Segment AC. The point from the altitude that intersects AC is Point D. BD is the height of our triangle, AC is the base.

2) Angle A is 60 degrees, and since Angle BDA is 90 degrees, Angle ABD is 30 degrees. We can use the 30-60-90 degree right triangle property for the triangle BDA.

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AB is 9 units, and it is opposite the 90 degree angle. This means that 2x=9, x = \frac{9}{2} ==> This then means that AD, the segment opposite the 30 degree angle in this triangle is \frac{9}{2} units. Segment BD (the height) is \frac{9}{2} * \sqrt3.

3) Angle C is 45 degrees, and Angle BDC is 90 degrees, which means that Angle CBD is 45 degrees. We can use the 45-45-90 degree right triangle property for the triangle BCD.

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4) Area is \frac{1}{2}*b*h, the base (b) is AC (which is \frac{9}{2}+\frac{9}{2}*\sqrt3), the height is BD (\frac{9}{2}*\sqrt3). When multiple you will get \frac{81}{4}*\sqrt3 + \frac{243}{4}, then this multiplied by 1/2 is

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