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Solve quadratic equation

Solve a quadratic equation

The math skill being taught is how to factor quadratic equations by identifying two numbers that both add to the coefficient of the linear term and multiply to the constant term. After splitting the linear term with these numbers, the equation is restructured into binomials for simpler solving.

Learn solve quadratic equation

Teaching Transcript

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Let's factor this quadratic equation into a pair of bracketed terms

The trick to factoring quadratic equations is to split the 'X' variables. We need to find two values that will add to our 'X' coefficient of negative 15.

And that also multiply to our constant of positive 56

Negative 8 and negative 7 meet that criteria, so those are the pair that we can split the negative 15 'X' into.

Let's rewrite our quadratic with the 'X' term split out

Now let's group into two binomials. Pay close attention to the sign on the second binomial. Since we're subtracting the entire bracket, and we started with a positive 56, we need that to be negative inside the brackets, because subtracting negative 56 is the same as positive 56.

We can remove a common factor of 'X' from the first bracket

And we can remove a common factor of 7 from the second

We now have the entire term in brackets, 'X' minus 8, as a common factor, so we can remove that and we have our answer

Skill Practice

Solve a quadratic equation

Test your understanding of solve quadratic equation by practicing it! Work through the below exercises to use it in practice.