Solve for x:
plus(SQUARE + "x^2") + plus( LINEAR + "x" ) + CONSTANT = 0
x = {}
and x = {}
The two numbers -A and -B satisfy both conditions:
\qquad \color{PINK}{-A} + \color{PINK}{-B} =
\color{GREEN}{SIMPLELINEAR}
\qquad \color{PINK}{-A} \times \color{PINK}{-B} =
\color{BLUE}{SIMPLECONSTANT}
(x A < 0 ? "+" : "" \color{PINK}{-A})
(x B < 0 ? "+" : "" \color{PINK}{-B}) = 0
Since the following equation is true we know that one or both quantities must equal zero.
(x A < 0 ? "+" : "" -A)
(x B < 0 ? "+" : "" -B) = 0
x + -A = 0 or x + -B = 0
Thus, x = A and x = B are the solutions.
Solve for x:
plus( SQUARE + "x^2") + plus( LINEAR + "x" ) + CONSTANT = 0
x = \quadA
The number -A used twice satisfies both conditions:
\qquad \color{PINK}{-A} + \color{PINK}{-A} =
\color{GREEN}{SIMPLELINEAR}
\qquad \color{PINK}{-A} \times \color{PINK}{-A} =
\color{BLUE}{SIMPLECONSTANT}
So (x + \color{PINK}{-A})^2 = 0.
So (x \color{PINK}{-A})^2 = 0.
x + -A = 0
Thus, x = A is the solution.
Dividing both sides by SQUARE gives:
x^2 + plus(SIMPLELINEAR + "x") + SIMPLECONSTANT=0
The coefficient on the x term is SIMPLELINEAR
and the constant term is SIMPLECONSTANT, so we need to find two numbers
that add up to SIMPLELINEAR and multiply to
SIMPLECONSTANT.