Question

Item 8 Solve for x. Use the quadratic formula. 2x2−5x−9=0 Enter the solutions, in simplified radical form, in the boxes.

Answer 1

5+√97/4

Also 5-√97/4

Explanation:

The Quadratic formula is x=-b+-√b^2-4ac/2a

This means that we should plug the values for A B AND C into the formula

We can work out that

A = 2

B=-5

C=-9

Once we have put these into the formula we get

5+√97/4 (all over 4) aka 3.71

Also 5-√97/4 (all over 4) aka -1.21

Answer 2

`\large\boxed{x=(5-√(97))/(4)\ or\ x=(5+√(97))/(4)}`

Explanation:

`\text{Let}\ ax^2+bx+c=0\\\\\text{The quadratic formula:}\\\\\Delta=b^2-4ac\\\\\text{If}\ \Delta>0,\ \text{then the equation has two solutions}\ x=(-b\pm\sqrt\Delta)/(2a)\\\\\text{If}\ \Delta=0,\ \text{then the equation has one solution}\ x=(-b)/(2a)\\\\\text{If}\ \Delta<0,\ \text{then the equation has no solution}\\==================================`

`\text{The equation}\ 2x^2-5x-9=0\\\\a=2,\ b=-5,\ c=-9\\\\\Delta=(-5)^2-4(2)(-9)=25+72=97>0\\\\\sqrt\Delta=√(97)\\\\x_1=(-(-5)-√(97))/(2(2))=(5-√(97))/(4)\\\\x_2=(-(-5)+√(97))/(2(2))=(5+√(97))/(4)`