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.

Want to master Microsoft Excel and take your work-from-home job prospects to the next level? Jump-start your career with our Premium A-to-Z Microsoft Excel Training Bundle from the new Gadget Hacks Shop and get lifetime access to more than 40 hours of Basic to Advanced instruction on functions, formula, tools, and more.

Buy Now (97% off) >

Our Best Phone Hacks

Gadget Hacks' tips — delivered daily.

2 Comments

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.

Share Your Thoughts

  • Hot
  • Latest