Solving Quadratic Equations by Completing the
Solve by completing the square: 3x2 - 30 = -21x
The solutions of 3x2 - 30 = -21x are
|Step 1 Isolate the x2-term and the x-term
on one side of the equation.
Add 21x to both sides.
Add 30 to both sides.
| 3x2 - 30 =
3x2 + 21x - 30 = 0
3x2 + 21x = 30
|Step 2 If the coefficient of x2 is not 1,
divide both sides of the equation
by the coefficient of x2.
Divide both sides by 3.
| x2 + 7x = 10
|Step 3 Find the number that completes
the square: Multiply the coefficient
of x by
. Square the result.
The coefficient of the x-term is 7.
|Step 4 Add the result of Step 3 to both
sides of the equation.
to both sides.
Simplify the right side.
The result is
|Step 5 Write the trinomial as the
square of a binomial.
|Step 6 Finish solving using the
Square Root Property.
Use the Square Root Property.
|For each equation, subtract
from both sides and simplify
|Step 7 Check each solution.
We leave the check for you.
To divide both sides of an equation by 3,
we divide each term by 3, like this:
We can use the â€œplus or minusâ€ symbol to
write the solutions like this