Topic B: Lessons 14-15: The quadratic formula
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Rewrite the equation 6x^2 + 3 = 2x - 6 in standard form and identify a, b, and c. So standard form for a quadratic equation is ax squared plus bx plus c is equal to zero. So essentially you wanna get all of the terms on the left-hand side, and then we want to write them so that we have the x terms...where their exponents are in decreasing order. So we have the x squared term and then the x term and then we have the constant term. So let's try to do this over here. So let me rewrite our original equation. We have 6x squared plus 3 is equal to 2x minus 6. So essentially we wanna get everything on the left-hand side. so I could subtract 2x from both sides, so I could subtract 2x from both sides, so let me just...I'll take one step at a time. So I can subtract 2x from both sides. And then I'll get...and I'm gonna write it in descending order for the exponents on x. So the highest exponent is x squared. So I'll write that first. 6x squared, and then we have minus 2x, and then we have plus 3 is equal to... the 2 'x's on the right cancel out...equal to negative 6. And now, to get rid of this negative 6 on the right-hand side, we can add 6 to both sides. So let's add 6 to both sides... ...and then this simplifies to 6x squared, minus 2x, plus nine is equal to...zero. So let's make sure we're already in standard form. All of our terms, our non-zero terms are on the left-hand side, we've done that. We have a zero on the right-hand side, we've done that. And, we have the x squared term first, then the x to the first power term, then the constant term. x squared, then x to the first, then the constant term. So we are in standard form. And so we can say that a is equal to 6, a is equal to 6. We could say that b is equal to, and this is key, it's not just the 2, it's the negative 2. B is equal to negative 2, 'cause notice this says plus bx, but over here we have minus 2x. So the b is a negative 2 here. B is negative 2. And then c, c is going to be, c is going to be 9.