HSA.REI.B.4 Tutor Intake — Solving Quadratic Equations

A student solves $(x - 3)^2 = 25$ and writes only $x = 8$.

What error did the student make?

A student is completing the square on $x^2 + 10x - 3 = 0$.
They write: $x^2 + 10x = 3$, then add $25$ to the left side to get
$x^2 + 10x + 25 = 3$.

What error did the student make?

The discriminant of a quadratic equation is $b^2 - 4ac = -7$.

What does this tell you about the solutions?

Solve $x^2 = 49$.

Enter both solutions separated by a comma (smaller value first):
$x = $   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   or $x = $   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲  

Use the quadratic formula to solve $x^2 - 5x + 6 = 0$.

Identify: $a = $   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   , $b = $   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   , $c = $   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲  

A student completes the square on $x^2 - 6x + 2 = 0$, arriving at
$(x - 3)^2 = 7$.

Which values of $x$ solve the original equation?

Compute the discriminant $b^2 - 4ac$ for the equation $2x^2 + 3x + 5 = 0$.

Enter the value of the discriminant.