Solve the equation by completing the square. Round to the nearest hundredth if necessary. x2 + 3x = 25

Question

asked Jun 16, 2019 33.2k views

1 Answer

Iamamused · Answer 1 · 2019-06-23T07:45:46+0000

we are given

x^2+3x=25

We can complete square

we can write it as

x^2+2*(3)/(2)*x=25

now, we can add both sides (3/2)^2

x^2+2*(3)/(2)*x+((3)/(2))^2=25+((3)/(2))^2

now, we can use formula

a^2+2*a*b+b^2=(a+b)^2

we can write it as

(x+(3)/(2))^2=25+((3)/(2))^2

(x+(3)/(2))^2=25+(9)/(4)

(x+(3)/(2))^2=(109)/(4)

now, we can take sqrt both sides

$\sqrt{(x+(3)/(2))^2}=\sqrt{(109)/(4) }$

we will get as

first solution:

x+(3)/(2)=(√(109))/(2)

x=-(3)/(2)+(√(109))/(2)

x=3.72

Second solution:

x+(3)/(2)=-(√(109))/(2)

x=-(3)/(2)-(√(109))/(2)

x=-6.72

so, solutions are

x=-6.72

x=3.72 ................Answer