Completing

the SquareSPI 3103.3.2 Solve quadratic equations and systems, and determine roots of a higher order polynomial.

SPI 3103.3.2

Solve quadratic equations and systems, and determine roots of a higher order polynomial.

Check for Understanding 3103.3.7

Solve quadratic equations by factoring, graphing, completing the square, extracting square roots and using the quadratic formula.

Completing the square is one of the methods used to solve quadratic equations.

The general form of a quadratic equation is

ax2 + bx + c = 0, a ≠ 0

Step 1Write the equation in the form ax2 + bx = –c

Step 2If a ≠ 1, divide each term of the equation by a.

Step 3Complete the Square – Take ½ of b, and square the result.– Add the result to both sides of the equation.

Step 4Factor the left side of the equation as a trinomial square; combine like terms on the right.

Step 5Solve the equation by taking the square root of both sides.

Solve x2 + 8x – 3 = 0 by completing the square.

x2 + 8x – 3 = 0x2 + 8x = 3x2 + 8x + 16 = 3 + 16(x + 4)2 = 19

√(x + 4)2 = √19

√(x + 4)2 = √19 x + 4 = ± √19

√(x + 4)2 = √19 x + 4 =

±√19 x = –4 ± √19