Use the quadratic formula to solve the equation.
–4x2 – 3x + 2 = 0
To solve the given equation -4x^2 - 3x + 2 = 0 using the quadratic formula, we need to first identify the values of a, b, and c in the general quadratic equation form ax^2 + bx + c = 0.
In this case, a = -4, b = -3, and c = 2.
Now we can substitute these values into the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
x = (-(−3) ± √((-3)^2 - 4(-4)(2))) / (2(-4))
x = (3 ± √(9 + 32)) / (-8)
x = (3 ± √(41)) / (-8)
Therefore, the solutions to the equation –4x^2 – 3x + 2 = 0 using the quadratic formula are:
x ≈ (-3 + √41) / -8
x ≈ (-3 - √41) / -8
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Certainly! I apologize for any confusion. Let's walk through the solution step by step.
The given equation is -4x^2 - 3x + 2 = 0.
To solve this equation using the quadratic formula, we need to identify the values of a, b, and c in the general quadratic equation formula ax^2 + bx + c = 0.
In our equation, a = -4, b = -3, and c = 2.
Now, let's substitute these values into the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values, we get:
x = (-(−3) ± √((-3)^2 - 4(-4)(2))) / (2(-4))
Simplifying:
x = (3 ± √(9 - (-32))) / (-8)
x = (3 ± √(9 + 32)) / (-8)
x = (3 ± √(41)) / (-8)
Therefore, the solutions to the equation –4x^2 – 3x + 2 = 0 using the quadratic formula are:
x ≈ (-3 + √41) / -8
x ≈ (-3 - √41) / -8
These are the two possible values of x that satisfy the given equation.
To solve the equation –4x^2 - 3x + 2 = 0 using the quadratic formula, we can follow these steps:
Step 1: Identify the coefficients of the quadratic equation:
a = -4 (coefficient of x^2)
b = -3 (coefficient of x)
c = 2 (constant term)
Step 2: Substitute the values into the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
Step 3: Calculate the discriminant (b^2 - 4ac):
Discriminant = (-3)^2 - 4(-4)(2)
= 9 + 32
= 41
Step 4: Determine the nature of the solutions based on the discriminant:
- If the discriminant is positive (greater than 0), then there will be two real solutions.
- If the discriminant is zero, then there will be one real solution.
- If the discriminant is negative, then there will be no real solutions (two complex solutions).
In this case, the discriminant (41) is positive, so there will be two real solutions.
Step 5: Substitute the values into the quadratic formula to find the solutions:
x = (-(-3) ± √(9 - 4(-4)(2))) / (2(-4))
= (3 ± √(9 + 32)) / -8
= (3 ± √41) / -8
Therefore, the solutions to the equation -4x^2 - 3x + 2 = 0 using the quadratic formula are:
x = (3 + √41) / -8
x = (3 - √41) / -8
To use the quadratic formula, which can be used to solve any quadratic equation, you need to follow a few steps:
Step 1: Identify the coefficients of the terms in the equation.
In this case, our equation is: -4x^2 - 3x + 2 = 0
So the coefficient of the x^2 term is -4, the coefficient of the x term is -3, and the constant term is 2.
Step 2: Substitute the coefficients into the quadratic formula.
The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a)
Substituting the values into the formula, we get:
x = (-(−3) ± √((−3)^2 - 4×(-4)×2)) / (2×(-4))
Step 3: Simplify and solve the equation.
x = (3 ± √(9 + 32)) / (-8)
x = (3 ± √(41)) / (-8)
So the solutions to the equation -4x^2 - 3x + 2 = 0 are x = (3 + √41) / -8 and x = (3 - √41) / -8.