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
Square the right side of the equation
Take the square root of the right side of the equation
Multiply the right side of the equation by a
x squared plus b/a times x plus (b/2 * a) squared = (-4ac)/(4a^2) + b^2/(4a^2) Common denominator
= (-4ac + b^2)/(4a^2) Square the right side of the equation