Math 154B Name_____________________
Completing the Square Worksheet
To solve ax2 + bx + c = 0 by "completing the square":
1) Put the variable terms are on the left of the equal sign, in standard form, and the constant term is on the right. So, get it into the form
cbxax2
.
2) Divide by “
a
”, so the coefficient of x2 is 1.
3) Take one-half the coefficient of the x-term, squaring it, and adding this quantity to both sides of the equation. Basically, add
2
2
b
to both sides.
4) Factor the Perfect Square Trinomial on the left side of the equation and simplify the right side. Remember, it always factors into
2
2
b
x
5) Use the principle of square roots
6) Solve the remaining equation
7) Check your answer in the original equation.
Solve each equation by completing the square.
1.
0152
2xx
2.
352
2xx
3.
2782 2xx
4.
148 2
xx
5.
6542 2xx
6.
146 2
xx
7.
082
2xx
8.
187
2xx
