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# Solving Equations

**Wed 16 Sep — A.6 Solving Equations
**

Solving Equations:

**Equation**is two expressions set equal to each other.

To

**solve**an equation means to find the values of the

variables in their domains that make the equation a

true statement. A solution

**satisfies**an equation.

3 types of equations:

**Conditional, identity, contradiction**

(Give Examples of each)

(Give Examples of each)

**Solve these:**

Solve:

Use the standard procedure. Ans: –3

We can also solve this graphically. Since we want the value of x that makes
these two expressions

equal, we could graph each and see where they intersect.

Rewrite this as follows:

Find value of x where f(x) = g(x) on the graph:

Solve:

ANS: Contradiction

Note how graphs are parallel lines. No soln.

Solve:

Solve:

Solve:

Solve:

Solve:

We can also solve a quadratic equation by Completing

the Square. All that means is that we construct a

perfect square from a given expression and then use

the square root method to solve.

To complete the square of take half of b,

square this, and then add it to the expression.

For example, to make a perfect square we add

We get which can be written
, a perfect square.

Solve by completing the square:

Solve by completing the square:

The standard form of a quadratic equation:

where a, b, c are real numbers

and a is not 0.

We can use completing the square to solve this

to get the quadratic formula:

Solve using quadratic formula:

Solve:

Solve: