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"Why might it be helpful to rearrange the equation so that one side is an expression and the other side is 0?" (It allows us to find the zeros of the function defined by that expression. The zeros correspond to the -intercepts of the graph.)

You "solve" a quadratic equation by figuring out "WHEN Y=0 what does X equal?"(x,0). That's why you set the equation to 0 and not any other number; to find the X-intercept(s) aka (x, 0) point(s).

Note that a quadratic equation has repeated root if b*b-4.0*a*c is equal to zero. However, if a is zero, the equation becomes a linear one whose only solution is -c/b if b is not zero. Otherwise, if b is zero, two cases are possible.

Zeros of the polynomial are the solution for which the equation is satisfied. In the case of quadratics, there are two roots or zeros of the equation. And if we put the values of roots or x on the left-hand side of the equation, it will equal to zero. Therefore, they are called zeros.

Basic Steps to Setting Up Equations Determine what the question is asking. Write down the relevant information in simple statements. Assign symbols to unknown values that need to be found. Determine how the statements relate to each other mathematically.

If you end with 0=0 , then it means that the left-hand side and the right-hand side of the equation are equal to each other regardless of the values of the variables involved; therefore, its solution set is all real numbers for each variable.

0:18 25:04 Algebra - How To Solve Equations Quickly! - YouTube YouTube Start of suggested clip End of suggested clip Now all we need to do is separate the 3 from the x the opposite of multiplication is division. So weMoreNow all we need to do is separate the 3 from the x the opposite of multiplication is division. So we need to divide both sides by 3.. So x is 12 divided by 3 which is 4. And this is the answer.

The values satisfying the equation are 5 and −2.