Question

I need help with my math homework --WARNING--English is not my first language, sorry if I make spelling mistakes in my questions :(

Answer 1

1. x = 4.5

2. x = 0.75 or x = -4.5

Step-by-step explanation:

The quadratic formula says the solutions of the equation with the form ax² + bx + c are:

`x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

So, if the equation is 4x² - 36x + 81, the value of each constant is

a = 4

b = -36

c = 81

Then, the solutions are

`\begin{gathered} x=\frac{-(-36)\pm\sqrt[]{(-36)^2-4(4)(81)}}{2(4)} \\ x=\frac{36\pm\sqrt[]{1296-1296}}{8} \\ x=\frac{36\pm\sqrt[]{0}}{8}=(36)/(8)=4.5 \end{gathered}`

It means that this equation has a unique solution x = 4.5

In the same way, if we have the equation 8x² + 30x = 27, we first need to subtract 27 from both sides, so:

8x² + 30x - 27 = 27 - 27

8x² + 30x - 27 = 0

Now, we can identify the values of a, b, and c.

a = 8

b = 30

c = -27

Therefore, the solutions of the equation are

`\begin{gathered} x=\frac{-30\pm\sqrt[]{(30^2)-4(8)(-27)}}{2(8)} \\ x=\frac{-30\pm\sqrt[]{900+864}_{}}{16} \\ x=\frac{-30\pm\sqrt[]{1764}}{16} \\ x=(-30\pm42)/(16) \\ \text{ The solutions are} \\ x=(-30+42)/(16)=(12)/(16)=0.75 \\ or \\ x=(-30-42)/(16)=(-72)/(16)=-4.5 \end{gathered}`

So, the solutions for each quadratic equation are:

1. x = 4.5

2. x = 0.75 or x = -4.5