Solving Quadratic Equations With Different Methods | Completing The Square |Quadratic Formula

Solving Quadratic equations
A quadratic equation can be written in the form ax^2+bx+c=0, where a, b and c are real constants, and a ≠ 0. Quadratic equations can have one, two or no real solutions.
To solve a quadratic equation by factorising:
Write the equation in the form ax^2+bx+c=0
Factorise the left–hand side
Set each factor equal to zero and solve to find the value(s) of x.

Some equations cannot be easily factorised. You can also solve quadratic equations using the quadratic formula.
The solutions of the equation
ax^2+bx+c=0 are given by the formula:

x=(-b±√(b^2-4ac))/2a
In ax^2+bx+c=0 are the constants a, b and c are called coefficients

** Please note: This video has a writing error at 30 minutes for the following equation.
2 + 0.8x - 0.04x^2;
0.04x^2+ 0.8x + 2;
0.04 ( x^2 - 20x ) + 2; the correct way of simplifying as (-ve) sign is outside the bracket which changes the sign of each term in the bracket. However, writing errors in the video is
-0.04 ( x^2 + 20x), which is incorrect.
However, the rest of the simplified equation in the video is correct

It is frequently useful to rewrite quadratic expressions by completing the square:
Completing the square is used to solve quadratic equations that cannot be factorised and allows the turning point to be found.
For example, express X squared plus eight X subtract seven in the form of brackets X plus a squared, plus b.
First, find the value of a.
To do this, halve the coefficient of X. Half of eight is four, so our expression starts with
brackets x plus four all squared.
If x plus four squared is expanded it becomes x squared plus eight x plus 16.
X squared plus eight x matches the first two terms of the original expression, but needs
adjusting for the extra 16.
So, 16 is subtracted to get the same value as the original expression.
So, our expression becomes: brackets x plus four all squared subtract 16, subtract seven,
which simplifies to x plus four squared subtract 23.
Simplify like terms to complete the square to get negative 23.
Completing the square allows the turning point of the quadratic function to be stated.
If the equation is in the form x plus a squared plus b, then the turning point is negative a, b.
If the equation is in the form x subtract a squared plus b, then the turning point is a, b.
For this example, the turning point is negative four, negative 23.

In algebra, letters are used to stand for values that can change (variables ) or for values that are not known ( unknowns ). A term is a number or letter on its own, or numbers and letters multiplied together,
Letters can be used to stand for unknown values or values that can change. Formulas can be written and equations solved in a range of problems in science and engineering.
Collecting like terms means simplifying terms in expressions in which the variables are the same.
5 x n and n x 5 are both written 5n
a x b and b x a are both written ab
5a, 7a, a, 12a,... are examples of like terms
5a, 7b, z, 12y,..... are examples of unlike terms
Collecting like terms means simplifying terms in expressions in which the variables are the same. In the expression 4a + 3b + 3a - 6b, the tears 4a and 3a are like tears, as are 3b and - 6b.
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