Question

What are the approximate solutions of 2x^2+9x=8 to the nearest hundredth

Answer 1

x = 0.76 or x= -5.26

Explanation:

Points to remember

Solution of a quadratic equation ax² + bx + c = 0

x = [-b ± √(b² - 4ac)]/2a

It is given a quadratic equation,

2x² + 9x = 8

⇒ 2x² + 9x - 8 = 0

To find the solution

Here a = 2, b = 9 and c = -8

x = [-b ± √(b² - 4ac)]/2a

= [-9 ± √(9² - 4*2*(-8))]/2*2

= [-9 ± √(81 +64)]/4

= [-9 ± √(145]/4

= [-9 ± 12.04]/4

x = [-9 + 12.04]/4 or x = [-9 - 12.04]/4

x = 0.76 or x= -5.26

Answer 2

x=0.76 or -5.26

Explanation:

You can apply the completing square method to solve this ;

`2x^2+9x=8\\\\`

Rewrite the equation with a zero like below

`2x^2+9x-8=0`

This is by taking 8 to the left side of the equation

Divide the terms by 2 in x²

`(2x^2)/(2) +(9x)/(2) -(8)/(2) =(0)/(2)`

`=x^2+4.5x-4=0`

Move the number term to the right side of the equation

`x^2+4.5x=4`

complete square on the lefts side of the equation, how?

`=((b^)/(2))^2 =((4.5)/(2) )^2=5.0625`

balance the equation by adding this value to the right side , in this form

`x^2+4.5x+5.0625=4+5.0625\\\\`

Factorize the left side

`(x+2.25)(x+2.25)=9.0625\\\\\\(x+2.25)^2=9.0625\\`

Eliminate the square on the left side

`x+2.25=√(9.0625)`

x+2.25= ± 3.010

Solve for x

x=+3.010-2.25=0.76

or

x=-3.010-2.25=-5.26