Question

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

Answer 1

Answer:

x = 0.76 or x= -5.26

Step-by-step 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

Answer:

x=0.76 or -5.26

Step-by-step 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

$\frac{2x^2}{2} +\frac{9x}{2} -\frac{8}{2} =\frac{0}{2}$

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

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?

$=(\frac{b^}{2})^2 =(\frac{4.5}{2} )^2=5.0625$

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

$x+2.25=\sqrt{9.0625}$

x+2.25= ± 3.010

Solve for x

x=+3.010-2.25=0.76

or

x=-3.010-2.25=-5.26