Question

Use the quadratic formula to find both solutions to the quadratic equation

given below.
4x² + 5x+1=0
A. X=-
-3-√√-7
8
□ B. x=-3-√7
8
C. x=
E. x=
-3+√√-7
8
D. x=-¹
+3+√7
8
F. x= -1

Answer 1

Answer: x=-1/4 and x=-1

Explanation:

The answer choices you give are extremely hard to figure out, so I hope my explanations and answers help.

The quadratic formula is
`x=(-b\pm√(b^2-4ac) )/(2a)`. Once we figure out a, b, c, we can plug them into the formula and solve for x.

The standard form equation is ax²+bx+c=0. The equation given matches this so we know that:

a=4

b=5

c=1

Plug them into the formula. There is a
`\pm` symbol, which stands for "plus or minus". This means we solve the formula with addition and subtractions separately. We should have 2 solutions at the end. Let's do them separately to show work.

Solution 1: addition

`x_1=(-5+√(5^2-4(4)(1)) )/(2(4))` [exponents]

`x_1=(-5+√(25-4(4)(1)) )/(2(4))` [multiply]

`x_1=(-5+√(25-16) )/(8)` [inside square root]

`x_1=(-5+√(9) )/(8)` [square root]

`x_1=(-5+3)/(8)` [add]

`x_1=(-2)/(8)` [divide top and bottom by 2]

`x_1=-(1)/(4)`

Solution 2: subtraction

`x_2=(-5-√(5^2-4(4)(1)) )/(2(4))` [exponents]

`x_2=(-5-√(25-4(4)(1)) )/(2(4))` [multiply]

`x_2=(-5-√(25-16) )/(8)` [inside square root]

`x_2=(-5-√(9) )/(8)` [square root]

`x_2=(-5-3)/(8)` [subtract]

`x_2=(-8)/(8)` [divide]

`x_2=-1`

I am not able to find the answer choices, but we know that x=-1/4 and x=-1.