On October 23rd, 2014, we updated our
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Solving for Roots By
Completing the square
• You can complete the square by adding a constant to both
sides of the equation
• Add the constant that will turn the quadratic into a perfect
• Take the square root of both sides
• Solve for x
Ex. Solve x2 4x + 2 = 0
When the leading coefficient is not equal to one
• Divide both sides of the equation by the
coefficient a before completing the square
Ex. Solve by completing the square 2x2 6x 7 = 0
General Solution to Quadratics by
Completing the Square
(building the quadratic formula)
Solve for x by completing the square
ax2 + bx +c = 0
The completing square allows us to find that we can find the
solutions using the
You can use the quadratic formula to solve any quadratic equation.
To use the equation you first need to set up the equation in
ax2 + bx + c = 0
Then you can substitute a, b, and c into the formula
Ex. Sove x2 + 3x 9 = 0
If you remember from our quadratics unit, we can
find the x value at the vertex, and the axis of
The quadratic formula can be represented by two
The first part is the h value.
The second part is the horizontal distance from the
axis of symmetry to the x intercepts in both the
and negative direction.