Question

The steps to derive the quadratic formula are shown below: Step 1 ax2 + bx + c = 0 Step 2 ax2 + bx = − c Step 3 x2 + b over a times x equals negative c over a Step 4 x2 + b over a times x plus b squared over 4 times a squared equals negative c over a plus b squared over 4 times a squared Step 5 x2 + b over a times x plus b squared over 4 times a squared equals negative 4 multiplied by a multiplied by c, all over 4 multiplied by a squared plus b squared over 4 times a squared Step 6 Provide the next step to derive the quadratic formula. x plus b over 2 times a equals plus or minus b squared minus 4 times a times c all over the square root of 4 times a squared x plus b over 2 times a equals plus or minus b minus 2 times a times c all over square root of 2 times a x plus b over 2 times a equals plus or minus the square root of the quantity b squared minus 4 times a times c all over the square root of 4 times a squared x plus b over 2 times a equals plus or minus the square root of the quantity b squared minus 4 times a times c all over the square root of 2 times a

Answer 1

Answer:

$x + \frac{b}{2a} = \frac{+/ - \sqrt{b^2-4ac} }{2a}$

Step-by-step explanation:

Step 1:

$ax^2+bx+c = 0$

Step 2:

$ax^2+bx = -c$

Step 3:

$\frac{ax^2+bx}{a} = \frac{-c}{a}$

Step 4:

Adding $\frac{b^2}{4a^2}$ to both sides to complete the square

$x^2 + \frac{bx}{a} + \frac{b^2}{4a^2} = \frac{-c}{a} + \frac{b^2}{4a^2}$

Step 5:

$x^2 + \frac{bx}{a} + \frac{b^2}{4a^2} = \frac{-4ac+b^2}{4a^2}$

Step 6:

Taking square root on both sides

$x + \frac{b}{2a} = \frac{+/ - \sqrt{b^2-4ac} }{2a}$