Learning Objectives:
1. Solve quadratic equations using the
Square Root Property.
2. Complete the square in one variable .
3. Solve quadratic equations by completing
the square.
4. Solve problems using the Pythagorean
Theorem.
Square Root Property: No longer the principle
square root.
If x2 = p, then |
Example: Solve the equation:
x2 = 36
Solving Quadratic Equations Using the Square
Root Property
Step 1: Isolate the ex pression containing the
square
term.
Step 2: Use the Square Root Method . Don’t forget
the ± symbol .
Step 3: Isolate the variable , if necessary.
Step 4: Check. Verify your solutions .
2. Square Root Property
Example: Solve the equation:
3x2 = 150
Check:
Example: Solve:
(2x + 3)2 =10
3. Completing the Square
The idea behind completing the square is to “adjust” the
left
side of a quadratic equation of the form x2 + bx + c in order to
make it a perfect square trinomial.
Obtaining a Perfect Square Trinomial
Step 1: Identify the coefficient of the first -degree term.
Step 2: Multiply this coefficient by
1/2
and then square the result.
Step 3: Add this result to both sides of the equation.
Solving a Quadratic Equation by Completing the Square
Step 1: Rewrite x2 + bx + c = 0 as x2 + bx = – c by
subtracting
the constant from both sides of the equation.
Step 2: Complete the square in the expression x 2 + bx by
making it a perfect square trinomial. Whatever you
add to the left side of the equation must also be added
to the right side.
Step 3: Factor the perfect square trinomial on the left
side.
Step 4: Solve the equation using the Square Root Property.
Step 5: Check. Verify your solutions.
Example: Solve: x2 – 6x – 7 = 0
Example: Solve: 2x2 + 5x – 3 = 0
4. Pythagorean Theorem
Pythagorean Theorem
In a right triangle, the square of the length of the
hypotenuse is equal to the sum of the squares of the
lengths of the legs.
c2 = a2 + b2
Example:
A baseball diamond is square. Each side of the square is
90 feet
long. How far is it from home plate to second base?
