Question

A portion of the quadratic formula proof is shown. Fill in the missing reason.

Statements Reasons
ax2 + bx + c = 0 Given
ax2 + bx = −c Subtract c from both sides of the equation
x squared plus b over a times x equals negative c over a Divide both sides of the equation by a
x squared plus b over a times x plus the quantity b over 2 times a squared equals negative c over a plus the quantity b over 2 times a squared Complete the square and add the quantity b over 2 times a squared to both sides
x squared plus b over a times x plus the quantity b over 2 times a squared equals negative c over a plus b squared over 4 times a squared Square the quantity b over 2 times a on the right side of the equation
x squared plus b over a times x plus the quantity b over 2 times a squared equals negative 4 times a times c over 4 times a squared plus b squared over 4 times a squared Find a common denominator on the right side of the equation
x squared plus b over a times x plus the quantity b over 2 times a squared equals b squared minus 4 times a times c all over 4 times a squared ?


Multiply the fractions together on the right side of the equation
Subtract 4ac on the right side of the equation
Add 4ac to both sides of the equation
Add the fractions together on the right side of the equation

Answer 1

The missing reason in the quadratic formula proof when combining terms over a common denominator is 'Combining like terms and simplification'.

Step-by-step explanation:

The missing reason in the proof of the quadratic formula where the equation x squared plus b over a times x plus the quantity b over 2 times a squared equals b squared minus 4 times a times c all over 4 times a squared is achieved through simplification and finding a common denominator on the right side of the equation. The accurate reason is Combining like terms and simplification. This step combines the result -4ac from the term negative 4 times a times c and the b squared from the term b squared over 4 times a squared, putting them over the common denominator 4 times a squared.