Question

evaluate the discriminant and determine the number and type of solutions to the equation.
$-2x^{2}+8x = 4$
progress: 0/2
part 1 of 2
discriminant: \boxed{}

Explanation:

Step1: Rewrite in standard form

Subtract 4 from both sides to get the quadratic equation in $ax^2+bx+c=0$ form:
$-2x^2 + 8x - 4 = 0$
We can simplify by multiplying through by -1:
$2x^2 - 8x + 4 = 0$
Here, $a=2$, $b=-8$, $c=4$.

Step2: Calculate discriminant

Use discriminant formula $\Delta = b^2 - 4ac$:
$\Delta = (-8)^2 - 4(2)(4)$
$\Delta = 64 - 32$
$\Delta = 32$

Step3: Analyze solution type

Since $\Delta = 32 > 0$ and 32 is not a perfect square, there are 2 distinct real irrational solutions.

Answer:

Discriminant: $32$
Number and type of solutions: 2 distinct real irrational solutions