complete the steps of the derivation of the quadratic formula

Question

Step 1: (x+b/za)^2-b^2-4ac/4a^2=0

step 2

step 3

step 4

Answer 1

Step 2: Expand (x+b/2a)^2 to get x^2 + 2bx/a + b^2/4a^2 - b^2 - 4ac/4a^2 = 0

Step 3: Simplify the equation by combining like terms to get x^2 + 2bx/a + b^2/4a^2 - b^2 - 4ac/4a^2 = 0

Step 4: Multiply through by 4a^2 to get 4a^2x^2 + 8abx + 4b^2 - 4a^2b^2 - 16ac = 0

Step 5: Rearrange terms to get the standard form of a quadratic equation: 4a^2x^2 + 8abx + 4ac = 0

Step 6: Divide through by 4a^2 to get x^2 + 2b/a x + c = 0

Step 7: Divide through by 4a^2 to get x^2 + (b/a)x + c = 0, which is the quadratic formula with a = 1: x = (-b ± √(b^2 - 4ac))/2a.