16.2c Quadratic Formula – Make Equation Equal Zero. Before using the quadratic formula the equation must equal zero, and be in standard form. Or in other words, it needs to be in descending order going from the largest exponent down to the smallest. That mean’s that the equation should look
like, ax squared plus bx plus c equals the zero. In example one here, notice that we have 2x squared by itself and there fifteen minus 7x on the other sides. So what we want to do is move these over, um, I always take the time to write this out because, otherwise I have the tendency to
get these wrong, and then when I write it out I put into descending order. So I have 2x squared plus 7x minus fifteen equal to zero. Now we put it into the quadratic formula. Which means we now have, x equal to plus or minus whops let’s fix that, opposite of our b plus or minus the square root of seven squared, minus four times our a times our c, all over our two times our a. So now we get, x equals negative seven plus or minus the square root of 169, all over four. So that means that x equals negative seven plus or minus the square root of 169 is thirteen, all over four. So, we have negative seven plus thirteen, which will give us six-fourths, and negative seven minus thirteen which would give us negative twenty-fourth. So that means x equals, three-halves and negative five. In example two: we need to move our seven over, so we’ll subtract seven from both sides. We now have 3x squared plus 5x minus five equal to zero. Using our quadratic formula, we have x equal to opposite of our b plus or minus our square root of b minus four times our a times our c, all over two times our a. Now that’s going to give us x equal to negative five plus or minus the square root of eighty-five, all over six. Let’s see eighty-five can we simplify that? No, we can’t simplify eighty-five, eighty-five is five times seventeen, neither wouldn’t…neither which would be squared. So that means that our answer will just be, x equal to negative five plus or minus the square root of eight-five, all over six.