Respuesta :

GoddessofDork

Steps

So firstly, we need to isolate the x terms onto one side. To do this, subtract 48 on both sides of the equation:

[tex]2x^2-20x=-48[/tex]

Next, divide both sides by 2:

[tex]x^2-10x=-24[/tex]

Next, we are gonna make the left side of the equation a perfect square. To find the constant of this soon-to-be perfect square, divide the x coefficient by 2 and then square the quotient. Add the result onto both sides of the equation:

[tex]-10 \div 2=-5\\(-5)^2=25\\\\x^2-10x+25=1[/tex]

Now, factor the left side:

[tex](x-5)^2=1[/tex]

Next, square root both sides of the equation:

[tex]x-5=\pm 1[/tex]

Next, add 5 to both sides of the equation:

[tex]x=5\pm 1[/tex]

Lastly, solve the left side twice -- once with the plus sign and once with the minus sign.

[tex]x=6,4[/tex]

Answer

In short, x = 6 and 4

tramserran

Answer: x = 4   x = 6

Step-by-step explanation:

2x² - 20x + 48 = 0

2x² - 20 x + _____ = -48 + ______      subtracted 48 from both sides

2(x² - 10x + _____ ) = 2(-24 + _____ )   factored out 2 from both sides

x² - 10x + _____  = -24 + _____          divided both sides by 2

x² - 10x + 25  = -24 +25          added 25 to both sides

       ↓        ↑            ↑

     [tex]\dfrac{-10}{2}=(-5)^2[/tex]     [tex]\bigg(\dfrac{b}{2}\bigg)^2[/tex] makes a perfect square

(x - 5)² = 1             simplified

[tex]\sqrt{(x-5)^2} =\sqrt{1}[/tex]    took square root of both sides

x - 5 = ± 1             simplified

x - 5 = 1       x - 5 = -1     split into two separate equations

   x = 6           x = 4       solved for x



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