Conner is correct because when 2 exponents with the same base are multiplied, you add the exponents (for example, (x^3)*(x^4) = (x^7)
![x=y^2+4y\\ y^2+4y-x=0\\\Delta=4^2-4\cdot1\cdot(-x)=16+4x\\\\ 1.\ \Delta0\\ \sqrt{\Delta}=\sqrt{16+4x}=\sqrt{4(4+x)}=2\sqrt{x+4}\\ y_1=\frac{-4-2\sqrt{x+4}}{2\cdot1}=-2-\sqrt{x+4}\\ y_2=\frac{-4+2\sqrt{x+4}}{2\cdot1}=-2+\sqrt{x+4}\\](https://tex.z-dn.net/?f=%20x%3Dy%5E2%2B4y%5C%5C%20y%5E2%2B4y-x%3D0%5C%5C%5CDelta%3D4%5E2-4%5Ccdot1%5Ccdot%28-x%29%3D16%2B4x%5C%5C%5C%5C%0A1.%5C%20%5CDelta%3C0%20%5CRightarrow%20y%5Cin%5Cemptyset%5C%5C%5C%5C%0A2.%20%5C%20%5CDelta%3D0%5C%5C%0Ay%3D-%5Cfrac%7B4%7D%7B2%5Ccdot1%7D%3D-2%5C%5C%5C%5C%0A3.%5C%20%5CDelta%3E0%5C%5C%0A%5Csqrt%7B%5CDelta%7D%3D%5Csqrt%7B16%2B4x%7D%3D%5Csqrt%7B4%284%2Bx%29%7D%3D2%5Csqrt%7Bx%2B4%7D%5C%5C%0Ay_1%3D%5Cfrac%7B-4-2%5Csqrt%7Bx%2B4%7D%7D%7B2%5Ccdot1%7D%3D-2-%5Csqrt%7Bx%2B4%7D%5C%5C%0Ay_2%3D%5Cfrac%7B-4%2B2%5Csqrt%7Bx%2B4%7D%7D%7B2%5Ccdot1%7D%3D-2%2B%5Csqrt%7Bx%2B4%7D%5C%5C)
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Answer:
See explanation
Step-by-step explanation:
Given
![-2(5x+8)=14+6x](https://tex.z-dn.net/?f=-2%285x%2B8%29%3D14%2B6x)
Required
Complete the steps
![-2(5x+8)=14+6x](https://tex.z-dn.net/?f=-2%285x%2B8%29%3D14%2B6x)
Multiply 5x and 8 by -2
![-10x - 16 = 14 + 6x](https://tex.z-dn.net/?f=-10x%20-%2016%20%3D%2014%20%2B%206x)
Subtract by 6x
![-10x - 6x- 16 = 14 + 6x - 6x](https://tex.z-dn.net/?f=-10x%20-%206x-%2016%20%3D%2014%20%2B%206x%20-%206x)
![-16x- 16 = 14](https://tex.z-dn.net/?f=-16x-%2016%20%3D%2014)
Add 16
![-16x- 16 + 16= 14 + 16](https://tex.z-dn.net/?f=-16x-%2016%20%2B%2016%3D%2014%20%2B%2016)
![-16x= 30](https://tex.z-dn.net/?f=-16x%3D%2030)
Divide by -16
![x= \frac{30}{-16}](https://tex.z-dn.net/?f=x%3D%20%5Cfrac%7B30%7D%7B-16%7D)
![x= -\frac{15}{8}](https://tex.z-dn.net/?f=x%3D%20-%5Cfrac%7B15%7D%7B8%7D)
<em>See attachment</em>
Answer:
![x = \frac{3}{4} + \frac{ \sqrt{105} }{4} \: \: , \: \: \: x = \frac{3}{4} - \frac{ \sqrt{105} }{4} \\](https://tex.z-dn.net/?f=x%20%3D%20%20%20%5Cfrac%7B3%7D%7B4%7D%20%2B%20%20%5Cfrac%7B%20%5Csqrt%7B105%7D%20%7D%7B4%7D%20%20%20%5C%3A%20%20%5C%3A%20%20%2C%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20x%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20%20%20-%20%20%5Cfrac%7B%20%5Csqrt%7B105%7D%20%7D%7B4%7D%20%20%5C%5C%20)
Step-by-step explanation:
2x² - 3x - 12 = 0
Using the quadratic formula which is
![x = \frac{ - b \pm\sqrt{ {b}^{2} - 4ac} }{2a} \\](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B%20-%20b%20%5Cpm%5Csqrt%7B%20%7Bb%7D%5E%7B2%7D%20%20-%204ac%7D%20%7D%7B2a%7D%20%20%5C%5C%20)
From the question
a = 2 , b = - 3 , c = - 12
So we have
![x = \frac{ - - 3\pm \sqrt{ ({ - 3})^{2} - 4(2)( - 12)} }{2(2)} \\ = \frac{3\pm \sqrt{9 + 96} }{4} \\ = \frac{3\pm \sqrt{105} }{4} \: \: \: \: \: \:](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B%20-%20%20-%203%5Cpm%20%5Csqrt%7B%20%28%7B%20-%203%7D%29%5E%7B2%7D%20%20-%204%282%29%28%20-%2012%29%7D%20%7D%7B2%282%29%7D%20%20%5C%5C%20%20%3D%20%20%5Cfrac%7B3%5Cpm%20%5Csqrt%7B9%20%2B%2096%7D%20%7D%7B4%7D%20%20%5C%5C%20%20%3D%20%20%5Cfrac%7B3%5Cpm%20%20%5Csqrt%7B105%7D%20%7D%7B4%7D%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%20%5C%3A%20%20)
Separate the solutions
We have the final answer as
![x = \frac{3}{4} + \frac{ \sqrt{105} }{4} \: \: , \: \: \: x = \frac{3}{4} - \frac{ \sqrt{105} }{4} \\](https://tex.z-dn.net/?f=x%20%3D%20%20%20%5Cfrac%7B3%7D%7B4%7D%20%2B%20%20%5Cfrac%7B%20%5Csqrt%7B105%7D%20%7D%7B4%7D%20%20%20%5C%3A%20%20%5C%3A%20%20%2C%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20x%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20%20%20-%20%20%5Cfrac%7B%20%5Csqrt%7B105%7D%20%7D%7B4%7D%20%20%5C%5C%20)
Hope this helps you
Answer:
A
Step-by-step explanation:
As the equation has already been factorised, we can find the value of x that results in 0 in each bracket:
x - 3 >= 0
x >= 3
x+2 >= 0
x >= -2