Question

Let ​ x^2+18x=44 .​ What values make an equivalent number sentence after completing the square?

Answer 1

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

$x^2 +18x + = 44+ \\ x^2+18x+( \frac{18}{2} )^2=44+( \frac{18}{2} )^2 \\ x^2+18x+9^2=44+9^2 \\ x^2+18x+81=44+81 \\ (x+9)^2=125$ - equivalent equation

Answer 2

Answer:

The value of x are 2.18 and -20.8.

Step-by-step explanation:

Given : Equation $x^2+18x=44$

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

Solution :

Equation $x^2+18x-44=0$

Applying completing the square,

Step 1 - Make the coefficient of x be 1

$x^2+18x-44=0$

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

i.e. square of 9

$x^2+18x-44+9^2-9^2=0$

Step 3 - Form the identity $(a^2+2ab+b^2)=(a+b)^2$

$x^2+2.9.x+9^2-44-81$

$(x+9)^2-125=0$

Completing the square form of the given equation is $(x+9)^2-125=0$

Now, we solve for x

$(x+9)^2=125$

$x+9=\sqrt{125}$

$x+9=\pm 11.18$

$x=\pm 11.18-9$

$x=11.18-9,-11.8-9$

$x=2.18,-20.8$

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