X²- 6x = 7 find the soultion to the equation by completing the square

x = - 1, x = 7

Step-by-step explanation:

Given

x² - 6x = 7

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 3) x + 9 = 7 + 9

(x - 3)² = 16 ( take the square root of both sides )

x - 3 = ± = ± 4

Add 3 to both sides

x = 3 ± 4, that is

x = 3 + 4 = 7 or x = 3 - 4 = - 1

x=-1 , x=7

Step-by-step explanation:

x²-6x-7=0

(x)² - 2(x)(3) +(3)² -7 - (3)²=0(adding and removing 9 to make it a complete square)

(x-3)² -7-9=0

(x-3)²-16=0

(x-3)² - (4)²= 0

(x-3+4)(x-3-4)=0

(x+1)(x-7)=0

(x+1)=0⇒x=-1

(x-7)=0⇒x=7

answer: solve 5\cdot 2^x=2405⋅2  

x

=2405, dot, 2, start superscript, x, end superscript, equals, 240.

solution

to solve for xxx, we must first isolate the exponential part. to do this, divide both sides by 555 as shown below. we do not multiply the 555 and the 222 as this goes against the order of operations!

\begin{aligned} 5\cdot 2^x& =240 2^x& =48 \\ \end{aligned}  

5⋅2  

x

2  

x

​    

=240

=48

​

step-by-step explanation: