Nonlinear equations, Solve for x

Algebra 1 Tutorial

Nonlinear equations, Solve for x

Intro

How do you solve a simple equation for x when an exponent is involved?

Sample Problem

Solve: X squared – 9x = 36

x=2, x=-18


x=-9, x=4


x=9, x=4


x= – 3 , x=12


x=6, x=-6


Solution

1. The first step in a problem like this is to get all factors on only one side of the equation. So, starting with x squared – 9x = 36, We subtract 36 from both sides of the equation. You get x squared – 9x -36 = 0 .

2. Next, you must factor the equation. Factoring means finding two numbers that when multiplied together equal a larger number. 36 is not a prime number, so it can be factored down. What times something else is 36?

2*18 = 36
3*12 = 36
4*9 = 36
6*6 = 36 .

But we are really trying to factor -36.
This means that one of the two number pairs above must be negative. Whenever you multiply a positive number by a negative number, you get a negative number. For example, 2* -18 = -36, and -4*9 = -36.

3. Next is a kind of juggling game. Out of all of the combinations of factors for -36, you must add each pair of factors together to see which one equals the number multiplied by x. Here this number is 9. So, adding a negative sign to the pairs of numbers, for example you would come up with some as follows:

2-18= -16
18-2 = 16
4-9= -5
9-4= 5
6-6=0.
Only one number combination is correct.

-3+12= 9. ( is the number we seek, so the correct answers are -3 and 12.

4. Check your answer for correctness. Plug in the numbers one by one:

x squared – 9x – 36 = 0

(-3) squared – 9*(-3) – 36 = 9 + 27 – 36. Simplify this: (9+27) – 36=
36-36 = 0. So -3 is right. Next, check out 12:

12 squared – 9*12 -36 = 144 – 108 – 36= 144 – (108+36) = 144-144 = 0.
Therefore, 12 is also the correct solution.



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