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

A. Rewrite the perfect square trinomial as a binomial squared on the left side of the equation

Explanation:

Answer 2

`x + (b)/(2a) = (+/ - √(b^2-4ac) )/(2a)`

Explanation:

Step 1:

`ax^2+bx+c = 0`

Step 2:

`ax^2+bx = -c`

Step 3:

`(ax^2+bx)/(a) = (-c)/(a)`

Step 4:

Adding
`(b^2)/(4a^2)` to both sides to complete the square

`x^2 + (bx)/(a) + (b^2)/(4a^2) = (-c)/(a) + (b^2)/(4a^2)`

Step 5:

`x^2 + (bx)/(a) + (b^2)/(4a^2) = (-4ac+b^2)/(4a^2)`

Step 6:

Taking square root on both sides

`x + (b)/(2a) = (+/ - √(b^2-4ac) )/(2a)`