Question

Please help! And show work so I can understand in the future please! Worth 20 points!!

Answer 1

X^2+8x=10, has to look like ()^2 = value:

(x+4)^2 = x^2+8x+16, you match first the x^2 and term with x, okay?

Now that 16 was not there (add zero!):

x^2+8x+16-16 = (x+4)^2 -16, finish the problem:

(x+4)^2 = 11+16=27, and x+4 = +/-sqrt(27) --->  x = -4+/-sqrt(27) = -4 +/-3*sqrt(3) if you prefer.

The quadratic formula is a direct answer:

x^2+8x-11=0

x = (-8 +/- sqrt( 8^4 -4*1*(-11)) ) / 2 = (-8 +/- sqrt(108))/2

sqrt(108)=sqrt(4*9*3) = 2*3*sqrt(3) = 6*sqrt(3)-->

x = (-8+/- 6*sqrt(3))/2 = - 4 +/- 3*sqrt(3)

Lesson: completing the square is longer and requires some algebra skills but it pays off. Quadratic formula does not need us to think! But it may be cumbersome. Both are good depending on the rpoblem.

Indeed the quadratic formula was invented completing the sqaure for a*x^2+b*x+c = 0

Finally, sqrt(3)~1.73, so you may approximate the solutions as -4+/-3*1.7 = -4 +/- 5.1 = -9.1, and 1.1