can I get help how to use these quadratic formulas??

Question

Can someone show me how to use the quadratic formula with these problems?? thanks a billion!!

question #1:
2x2 + 4x = -1

question #2:
2x(x + 2) = 5

thank you soo much for everything!!!

Answer 1

Is question #1 2x^2+4x=-1?

If so, add 1 to both sides b/c you can't use the quadratic formula until you have ax^2+bx+c=0.

2x^2+4x+1=0

Now, a=2, b=4, and c=1 go into the QF:

x=(-4+/-sqrt(4^2-4*2*1))/(2*2)
x=(-4+/-sqrt(16-8))/(4)
x=(-4+/-sqrt(8))/(4)
x=(-4+/-2sqrt(2))/(4) b/c sqrt(8)=sqrt(4*2)=2sqrt(2)
x=(-2+/-sqrt(2))/(2) b/c you can cancel a 2 out of all terms

For question 2, distribute the 2x and then move the 5 over to the other side:
2x(x + 2) = 5
2x^2+4x=5
2x^2+4x-5=0

NOw a=2, b=4, and c=-5 so

x=(-4+/-sqrt(4^2-4*2*-5))/(2*2)
x=(-4+/-sqrt(16+40))/(4)
x=(-4+/-sqrt(56))/(4)
x=(-4+/-2sqrt(14))/(4) b/c sqrt(56)=sqrt(4*14)=2sqrt(14)
x=(-2+/-sqrt(14))/(2) b/c a 2 can be cancelled out of all terms

Answer 2

I'll help with #2
Distribute and move all terms to the left hand side so that we have a quadratic expression = 0.
2x^2 + 4x - 5 = 0
a = 2, b = 4, c = -5
Dump into quadratic formula
[-4 +- sqrt(4^2 - 4 * 2 * -5)] / (2*2)
[-4 +- sqrt(56)] / 4
[-4 +- 2sqrt(14)] / 4
Divide out a common factor of 2 from each term
[-2 +- sqrt(14)] / 2

Answer 3

Question 1 :
2x2 + 4x = -1
2x (x + 2) = -1
2x = -1 , x + 2 = -1
x = -1 / 2 , x = -1 -2 = -3
x = -0.5 & -3

Question 2 :
2x ( x + 2) = 5
2x = 5 , x + 2 = 5
x = 5 / 2 , x = 5 - 2 = 3
x = 2.5 & 3

Answer 4

2x² + 4x = -1

add 1 to both sides

2x² + 4x +1 = 0

solve with quadratic formula as you asked.

ax² + bx + c = 0
x = (-b ± √(b² - 4ac))/2a

x = (-4 ± √(16 - 8))/4

x = (-4 ± √(8))/4

x = -1 ± √(2)/2


2x(x + 2) = 5

expand and subtract 5 from both sides

2x² + 4x - 5 = 0

ax² + bx + c = 0
x = (-b ± √(b² - 4ac))/2a

x = (-4 ± √(16 + 40))/4

x = (-4 ± √(56))/4

x = (-4 ± 2√(14))/4

x = -1 ± √(14)/2
.

Answer 5

standard quadratic equation is ax^2 + bx + c where a,b,c are constants

I'll help with #1

2x^2 +4x = -1

standard form

2x^2 + 4x +1 = 0 a=2 b=4 and c=1.... you know the formula plug it in... afterwards find the answer to problem two.