How do you solve #4x^2+9x+5=0# using the quadratic formula?

Question

Hazel Anglin · Accepted Answer

#" "x= -10/8" and "-1#

Given that the standard form equation is: #y=ax^2+bx+c#

The #x=(-b+-sqrt(b^2-4ac))/(2a)#

Given equation:#" "y=4x^2+9x+5#

So:#" "a=4" ; "b=9" ; "c=5#

Thus by substitution:

#" "x=(-9+-sqrt(9^2-4(4)(5)))/(2(4))#

#" "x=(-9+-sqrt(81-80))/(8)#

#" "x=(-9+-1)/8#

#" "x= -10/8" and "-1#

Eli Assouline · Answer

undefined To solve the quadratic equation $4x^2 + 9x + 5 = 0$ using the quadratic formula, which is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, where $a$, $b$, and $c$ are the coefficients of the quadratic equation $ax^2 + bx + c = 0$, follow these steps:

1. Identify the values of $a$, $b$, and $c$ from the given equation. In this case, $a = 4$, $b = 9$, and $c = 5$.

2. Substitute these values into the quadratic formula to get $x = \frac{-9 \pm \sqrt{9^2 - 4 \times 4 \times 5}}{2 \times 4}$.

3. Simplify the expression inside the square root to get $x = \frac{-9 \pm \sqrt{81 - 80}}{8}$, which simplifies further to $x = \frac{-9 \pm \sqrt{1}}{8}$.

4. Since the square root of 1 is 1, the expression simplifies to $x = \frac{-9 \pm 1}{8}$.

5. Calculate the two possible values for $x$: $x_1 = \frac{-9 + 1}{8}$ and $x_2 = \frac{-9 - 1}{8}$.

6. Simplify to get $x_1 = \frac{-8}{8} = -1$ and $x_2 = \frac{-10}{8} = -\frac{5}{4}$.

Therefore, the solutions to the equation $4x^2 + 9x + 5 = 0$ are $x = -1$ and $x = -\frac{5}{4}$.

Eva Abramson · Answer

undefined To solve the quadratic equation 4x^2 + 9x + 5 = 0 using the quadratic formula:

1. Identify the coefficients a, b, and c in the quadratic equation: 
   a = 4, b = 9, c = 5.

2. Apply the quadratic formula: 
   x = (-b ± sqrt(b^2 - 4ac)) / (2a).

3. Substitute the values of a, b, and c into the quadratic formula:
   x = (-(9) ± sqrt((9)^2 - 4(4)(5))) / (2(4)).

4. Calculate inside the square root:
   b^2 - 4ac = (9)^2 - 4(4)(5) = 81 - 80 = 1.

5. Substitute the result into the quadratic formula:
   x = (-9 ± sqrt(1)) / 8.

6. Simplify the expression inside the square root:
   sqrt(1) = 1.

7. Solve for both possible values of x:
   x₁ = (-9 + 1) / 8 = -8 / 8 = -1.
   x₂ = (-9 - 1) / 8 = -10 / 8 = -5/4.

Therefore, the solutions to the equation 4x^2 + 9x + 5 = 0 using the quadratic formula are x = -1 and x = -5/4.