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

Answer:

$x_1=\frac{5+\sqrt{33}}{4}$≈2.69

$x_2=\frac{5-\sqrt{33}}{4}$≈-0.19

Step-by-step 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:

$x_1=\frac{5+\sqrt{33}}{4}$≈2.69

$x_2=\frac{5-\sqrt{33}}{4}$≈-0.19

Answer 2

Answer:

x = 2.69 or -.19

Step-by-step 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}.