Question

algebra 1 sem2
lesson 3.4 - solving quadratics with the quadratic formula
< 7 of 7 1 2 3 4 5 6 7
practice solving a quadratic equation that requires rearranging.
solve $2x^2 - 4x = 8$ using the quadratic equation. if you have a square root that does not simplify as a whole number evenly, round to the nearest tenth (1 decimal place).
write your answer as x=, x= (for example: x=2, x=-3).

Explanation:

Step1: Rearrange to standard form

$2x^2 - 4x - 8 = 0$
Simplify by dividing by 2: $x^2 - 2x - 4 = 0$

Step2: Identify coefficients

For $ax^2+bx+c=0$, $a=1$, $b=-2$, $c=-4$

Step3: Apply quadratic formula

Quadratic formula: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
Substitute values: $x=\frac{-(-2)\pm\sqrt{(-2)^2-4(1)(-4)}}{2(1)}$

Step4: Calculate discriminant

$\sqrt{4 + 16}=\sqrt{20}\approx4.472$

Step5: Compute two solutions

First solution: $x=\frac{2 + 4.472}{2}=\frac{6.472}{2}\approx3.2$
Second solution: $x=\frac{2 - 4.472}{2}=\frac{-2.472}{2}\approx-1.2$

Answer:

$x=3.2$, $x=-1.2$