LESSON 4-6A:
SOLVING QUADRATIC EQUATIONS BY FINDING SQUARE ROOTS
Review: Simplify each radical expression.
1)
2)
3)
[Perfect Squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, …]
4)
5) 4
6) 6
When the value b in ax2 + bx + c = 0 is zero (ax2 + c = 0), you can solve the quadratic equation by
solving for x2 and finding square roots.
Examples/Practice: Solve each quadratic equation by finding square roots.
1) 4x2 + 10 = 46
2) 3x2
5 = 25
3) 7x2
4) 2x2 + 9 = 13
5) 5x2
40 = 0
6) 3x2 + 8 = 44
Examples/Practice: Solving a Perfect Square Trinomial Equation
1) x2 + 4x + 4 = 25
2) x2
14x + 49 = 25
3) x2 + 8x + 16 = 10
4) x2
4x + 4 = 100
10 = 25
LESSON 4-6B:
COMPLETING THE SQUARE
You can form a perfect square trinomial from x2 + bx by adding
x2 + bx +
.
=
Examples/Practice: Complete the square.
1) x2 + 18x +
2) x2 + 6x +
3) x2
8x +
4) x2 + 5x +
5) x2
6) x2
3x +
10x +
STEPS FOR SOLVING AN EQUATION BY COMPLETING THE SQUARE
1) Rewrite the equation in the form x2 + bx = c. The coefficient of x2 must be 1 in
order to complete the square. Divide all the terms of the equation by the coefficient of x2
if it is not 1.
2) Complete the square by adding
to each side of the equation.
3) Factor the trinomial.
4) Find square roots.
5) Solve for x.
Examples/Practice: Solve each quadratic equation by completing the square.
1) x2 + 6x
3) 3x2
3=0
12x + 6 = 0
2) x2 + 12 = 10x
4) x2
5x = x
5
Examples/Practice: Solve each quadratic equation by completing the square.
5) 2x2
x+3=x+9
7) 3x2 + 15x
6=0
6) 4x2 + 10x = 12
8) 2x2
12x
8=0