how do you solve quadratic equations
Hlep
The quadratic equation always works,but factoring can do it also, if the factors are easy.
http://www.purplemath.com/modules/solvquad.htm
Put it in the form ax^2 + bx + c = 0
If you cannot factor it easily into two momialsw, then use this "quadratic equation" for the two solutions.
x = [-b +/- sqrt(b^2-4ac)]/2a
+/- means "plus or minus"
"sqrt" means "square root of"
They should me teaching you thisw equation as part of your algebra course.
To solve a quadratic equation, you can use different methods, such as factoring, completing the square, or using the quadratic formula. Here, I will explain how to use the quadratic formula.
The quadratic formula is given by:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
To solve a quadratic equation using the quadratic formula, follow these steps:
1. Identify the coefficients of the quadratic equation. Remember that the standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants.
2. Plug these coefficients into the quadratic formula.
3. Simplify the expression within the square root (b^2 - 4ac) to calculate the discriminant.
4. If the discriminant is positive, you will have two real and distinct solutions. If it is zero, you will have one real solution (known as a repeated root). And if it is negative, you will have two complex solutions.
5. Calculate the two solutions by evaluating (-b ± sqrt(b^2 - 4ac)) / (2a).
Let's go through an example to illustrate the process:
Example: Solve the quadratic equation x^2 - 3x - 4 = 0.
Step 1: Identify the coefficients a, b, and c:
a = 1, b = -3, c = -4
Step 2: Apply the quadratic formula:
x = (-(-3) ± sqrt((-3)^2 - 4(1)(-4))) / (2(1))
Step 3: Simplify the expression within the square root:
x = (3 ± sqrt(9 + 16)) / 2
Step 4: Calculate the discriminant:
Discriminant = b^2 - 4ac = (-3)^2 - 4(1)(-4) = 9 + 16 = 25
The discriminant is positive (25), so we will have two real and distinct solutions.
Step 5: Calculate the solutions:
x = (3 ± sqrt(25)) / 2
x1 = (3 + 5) / 2 = 8 / 2 = 4
x2 = (3 - 5) / 2 = -2 / 2 = -1
Therefore, the solutions to the quadratic equation x^2 - 3x - 4 = 0 are x = 4 and x = -1.