How To: Solve quadratic equations by factoring

Solve quadratic equations by factoring

This is a great educational video on how to solve quadratic equations by factoring. Let us take an example and try to learn the method. Here is a quadratic equation: (r+7) (r-9) = 0. Consider zero-factor property. For real a and b, if a.b = 0, then a = 0 or b = 0 or both are equal to zero. So r+7 = 0 or r-9 = 0 > r = -7 or r = 9. Hence, r = -7, 9. Similarly to solve a quadratic equation (13r+7) (6r-18) = 0, we will get 13r = -7 or r = -7 over 13. Also 6r = 18 or r = 3. So r= -7over 13, 3. This video will be very useful for the school students.

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To solve quadratic equations in standard form ax^2 + bx + c = 0 that can be factored, there is a new "Transforming Method" recently introduced on Yahoo or Google Search. This is may be the simplest and fastest method so far. Its strong points are: systematic, no guessing, no factoring by grouping, and no solving binomials. See the articles titled:"Solving quadratic equations by the new Transforming Method" on Yahoo or Google Search.

Solving quadratic equations by the new Transforming Method.
This method proceeds through 3 steps.

STEP 1. Transform the equation ax^2 + bx + c = 0 (1) into the simplified one x^2 + bx + ac = 0 (2), with a = 1, and C = ac.

STEP 2. Solve the transformed equation (2) by the Diagonal Sum Method (Yahoo or Google Search) that immediately obtains the 2 real roots y1 and y2 of equation (2).

STEP 3. Divide both y1 and y2 by the coefficient a to get the 2 real roots x1 and x2 of the original equation (1): x1 = y1/a, and x2 = y2/a.

Example. Solve: 24x62 + 59x + 36 = 0 (1). Transformed equation: x^2 = 59x + 864. (2). Both roots are negative (recall the Rule of Signs for Real Roots). Compose factor pairs of ac = 864 with all negative numbers. To save time, start from the middle of the factor chain. Proceeding: .....(-18, -48)(-24, -36)(-27, -32). This last sum is -27 - 32 = -59 = -b. Then, the 2 real roots of (2) are y1 = -27 and y2 = -32. Back to the original equation (1), the 2 real roots are: x1 = y1/24 = -27/24 = -9/8,, and x2 = y2/24 = -32/24 = -4/3.

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