How do you solve the following equation
x2 - 5x = 14
x2 - 5 x - 14 = 0
(x - 7) (x + 2) = 0
x = 7 or x = -2
How do I explain this to my son who was not taught this way???
How about asking him to give you two numbers which when multiplied will give you zero.
He would have to admit that one of them has to be zero.
Now point out that is exactly what your second last line in your solution says
You might want to put in the extra line of
therefore x-7 = 0 or x+2 = 0
then x = 7 or x = -2
(are they using the quadratic formula exclusively to solve a quadratic?)
To explain this method of solving equations to your son, you can follow these steps:
1. Start with the given equation: x^2 - 5x = 14.
2. Rearrange the equation to bring all the terms to one side, so you have x^2 - 5x - 14 = 0. Now, we have a quadratic equation in the form of ax^2 + bx + c = 0.
3. Next, we need to factorize the quadratic expression. Split the middle term (-5x) into two terms whose coefficients multiply to give the product of the coefficient of x^2 (which is 1) and the constant term (which is -14). In this case, the factors are -7 and 2, since -7 * 2 = -14 and -7 + 2 = -5. So the factored form becomes (x - 7)(x + 2) = 0.
4. Now, apply the zero product property, which states that if a product of any numbers is equal to zero, then at least one of the numbers must be zero. Therefore, either (x - 7) = 0 or (x + 2) = 0.
5. Solve each equation separately to find the possible values of x. For (x - 7) = 0, add 7 to both sides of the equation, resulting in x = 7. For (x + 2) = 0, subtract 2 from both sides to get x = -2.
So, the solutions to the original equation are x = 7 and x = -2.