Respuesta :

Bladerunner1976
To find the final term to compete the square you need to divide the 'x' term by 2 then square it

[tex]x^2 +18x + = 44+ \\ x^2+18x+( \frac{18}{2} )^2=44+( \frac{18}{2} )^2 \\ x^2+18x+9^2=44+9^2 \\ x^2+18x+81=44+81 \\ (x+9)^2=125[/tex] - equivalent equation

Answer:

The value of x are 2.18 and -20.8.

Step-by-step explanation:

Given : Equation [tex]x^2+18x=44[/tex]

To find : What values make an equivalent number sentence after completing the square?

Solution :

Equation [tex]x^2+18x-44=0[/tex]

Applying completing the square,

Step 1 - Make the coefficient of x be 1

[tex]x^2+18x-44=0[/tex]

Step 2 - Add and subtract the square of  half of the coefficient of x

i.e. square of 9

[tex]x^2+18x-44+9^2-9^2=0[/tex]

Step 3 - Form the identity [tex](a^2+2ab+b^2)=(a+b)^2[/tex]

[tex]x^2+2.9.x+9^2-44-81[/tex]

[tex](x+9)^2-125=0[/tex]

Completing the square form of the given equation is [tex](x+9)^2-125=0[/tex]

Now, we solve for x

[tex](x+9)^2=125[/tex]

[tex]x+9=\sqrt{125}[/tex]

[tex]x+9=\pm 11.18[/tex]

[tex]x=\pm 11.18-9[/tex]

[tex]x=11.18-9,-11.8-9[/tex]

[tex]x=2.18,-20.8[/tex]

Therefore, The value of x are 2.18 and -20.8.

Otras preguntas