Question

Solve each equation using the quadratic formula. Find the exact solution, then approximate the solution to the nearest hundredth.

2x^2 - 1 =5x

I need an answer like this:

Answer 1

x = 2.69 or -.19

Explanation:

Given equation is :

2x²-1 =5x

Adding -5x to both sides of above equation,we get

2x²-1-5x =5x-5x

2x²-5x-1 =0

ax²+bx+c = 0 is general quadratic equation.

x =(-b±√b²-4ac) / 2a is solution of general equation.

Comparing general equation with given quadratic equation,we get

a = 2, b = -5 and c = -1

Putting above values in quadratic formula,we get

x = (-(-5)±√(-5)²-4(2)(-1)) / 2(2)

x = ( 5± √25+8) / 4

x = ( 5± √33) / 4

x = (5±5.745) /4

x = (5+5.745) / 4 or x = (5-5.745) / 4

x = 10.745 / 4 or x = -.745/4

x = 2.686 or -0.186

Round 2.686 to 2.69 and -0.186 to -0.19

Hence, the solution of 2x²-1= 5x is {2.69,-0.19}.

Answer 2

`x_1=(5+√(33))/(4)`≈2.69

`x_2=(5-√(33))/(4)`≈-0.19

Explanation:

To solve this problem you must apply the proccedure shown below:

1. You have that the quadratic formula is:

`x=\frac{-b+/-\sqrt{b^(2)-4ac}}{2a}`

2. To solve the quadratic equation you must substitute the values. So, you have that:

Rewrite the equation:

`2x^(2)-5x-1=0`

`a=2\\b=-5\\c=-1`

Then you have:

`x=\frac{-(-5)+/-\sqrt{(-5)^(2)-4(2)(-1)}}{2(2)}`

3. Therefore, you obtain the following result:

`x_1=(5+√(33))/(4)`≈2.69

`x_2=(5-√(33))/(4)`≈-0.19