# Example 1: Using the quadratic formula | Quadratic equations | Algebra I | Khan Academy

Use the square formula to solve the equation, 0 = -7q ^ 2 + 2q + 9 Now, the quadratic formula, applies to any Quadratic equation for an image – we can put 0 on The left side 0 = ax ^ 2 + bx + c We generally deal with x, in this matter we are We deal with q But the quadratic formula says, look, if we have Quadratic equation for this image, as solutions This equation will be x equals -b + or – square root of b ^ 2 – 4ac – all divided by 2a These are two solutions, because There is one solution when we take the positive square root Another solution when we take Negative root It gives you both this radical If we look at the quadratic equation that we need to solve We can have a typical compatibility We deal with q and not x, but that’s the same the general idea It can be x if you want to And if you look at it, the -7 corresponds to a That is a It is the coefficient of the second degree expression 2 correspond to b It corresponds to the phrase first-class Then 9 corresponds to c It’s hard So let’s apply the quadratic formula That squared formula will tell us that solutions –q that achieves this equation – q will be equal -b b = 2 + Or – the square root of b ^ 2, that is, of 2 ^ 2 – 4 x a x -7 x c, i.e. 9 And all of that divided by 2a All this divided by 2 x a, which is once Other is -7 Equals -7 Then we have to evaluate these So this equals -2 + or – The square root of– let’s see, 2 ^ 2 = 4– and If we take this part, if we just take it -4 x -7 x 9, this is negative and That negative will be deleted The number becomes positive And 4 x 7 x 9 4 x 9 = 36 36 x 7 Let’s do this above here 36 x 7 7 x 6 = 42 7 x 3, or 3 x 7 = 21 + 4 = 25 252 So this becomes 4 + 252 Remember, we have -7 and We have a negative signal outside That is omitted, which is why we have positive 252 For this part here Then the denominator, 2 x -7 = -14 Now how much is this? How much is this? Well, we have this equal to -2 + or – The square root of – How much is 4 + 252? It’s 256 All this divided by -14 What are the 256? What is the square root of 256? He is 16 We can try that It’s 16 x 16 The square root of 256 is 16 So we can write everything as equals -2 + 16 / -14 Or -2 – right? It is positive 16/14 O-16 / positive 14 If you think of it as positive or negative, then this positive is the positive over there And if you have that negative, then that negative is That minus is over there Now we have to evaluate these two numbers We just have to evaluate them -2 + 16 = 14, ÷ -14 = -1 So q is -1 Or -2 – 16 = -18, ÷ -14 = 18/14 – Negative signals are deleted – the equivalent of 9/7 So q = -1, or it could It equals 9/7 And you can try them, substitute those q values \u200b\u200binto The original equation, and urge yourself of it Check it out We can try with the first value If we take q = -1 -7 x -1 ^ 2 – -1 ^ 2 = 1– So this is -7 x 1, right? It -1 ^ 2 -1 x 2 = -2, + 9 It’s 7 – 2, equal to -9, + 9 It really equals 0 We have verified it It will give you the opportunity to verify that 9 / 7 We will also be successful