79.7k views
4 votes
If the quadratic formula is used to solve 2x(x + 5) = 4, what are the solutions? {-1/2, -9/2}

2 Answers

6 votes
x²+bx=c
x=[-b+√(b²+4c)]/2

2x(x+5)=4
2x²+10x=4
x²+5x=2

x=[-5+√(5²+4*4)]/2

if b=-1/2 and c=-9/2
x= {1/2+√[(1/2)²+4*(-9/2)]}/2


User Syd
by
9.0k points
4 votes

Answer:

The solutions are:


x=-5.372\ and\ x=0.372

Explanation:

The equation is given by:


2x(x+5)=4

on using the distributive property of multiplication in the left hand side of the equation we have:


2x* x+2x* 5=4\\\\i.e.\\\\2x^2+10x=4\\\\i.e.\\\\2x^2+10x-4=0\\\\i.e.\\\\2(x^2+5x-2)=0\\\\i.e.\\\\x^2+5x-2=0

Now, we know that the solution of the quadratic equation:


ax^2+bx+c=0 is given by:


x=(-b\pm √(b^2-4ac))/(2a)

Here we have:


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

Hence, the solution is:


x=(-5\pm √(5^2-4* 1* (-2)))/(2* 1)\\\\i.e.\\\\x=(-5\pm √(25+8))/(2)\\\\i.e.\\\\x=(-5\pm √(33))/(2)\\\\x=(-5+√(33))/(2),\ x=(-5-√(33))/(2)

Hence, in decimal for the solution is:


x=-5.372\ and\ x=0.372

User Gabriele Petrioli
by
7.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories